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tan(θ+10)=cot(2θ-10)

الحلّ

tan (θ + 1 0^{\circ}) = cot (2 θ - 10)

الحلّ

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}, θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

راديان

θ = \frac{4 π}{27} + \frac{10}{3} + \frac{2 π}{3} n, θ = \frac{13 π}{27} + \frac{10}{3} + \frac{2 π}{3} n

خطوات الحلّ

tan (θ + 1 0^{\circ}) = cot (2 θ - 10)

من الطرفين

cot (2 θ - 10)

اطرح

tan (θ + 1 0^{\circ}) - cot (2 θ - 10) = 0

sin, cos :

عبّر بواسطة

- cot (- 10 + 2 θ) + tan (1 0^{\circ} + θ)

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - \frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} + tan (1 0^{\circ} + θ)

tan (x) = \frac{sin ( x )}{cos ( x )}

:Use the basic trigonometric identity

= - \frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} + \frac{sin ( 1 0 ^{\circ} + θ )}{cos ( 1 0 ^{\circ} + θ )}

- \frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} + \frac{sin ( 1 0 ^{\circ} + θ )}{cos ( 1 0 ^{\circ} + θ )}

بسّط:

\frac{- cos ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} ) + sin ( \frac{18 0 ^{\circ} + 18 θ}{18} ) sin ( 2 θ - 10 )}{sin ( 2 θ - 10 ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}

- \frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} + \frac{sin ( 1 0 ^{\circ} + θ )}{cos ( 1 0 ^{\circ} + θ )}

\frac{sin ( 1 0 ^{\circ} + θ )}{cos ( 1 0 ^{\circ} + θ )} = \frac{sin ( \frac{18 0 ^{\circ} + 18 θ}{18} )}{cos ( \frac{18 0 ^{\circ} + 18 θ}{18} )}

\frac{sin ( 1 0 ^{\circ} + θ )}{cos ( 1 0 ^{\circ} + θ )}

1 0^{\circ} + θ

وحّد:

\frac{18 0 ^{\circ} + 18 θ}{18}

1 0^{\circ} + θ

θ = \frac{θ 18}{18}

:حوّل الأعداد لكسور

= 1 0^{\circ} + \frac{θ \cdot 18}{18}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{18 0 ^{\circ} + θ \cdot 18}{18}

= \frac{sin ( 1 0 ^{\circ} + θ )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )}

1 0^{\circ} + θ

وحّد:

\frac{18 0 ^{\circ} + 18 θ}{18}

1 0^{\circ} + θ

θ = \frac{θ 18}{18}

:حوّل الأعداد لكسور

= 1 0^{\circ} + \frac{θ \cdot 18}{18}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{18 0 ^{\circ} + θ \cdot 18}{18}

= \frac{sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )}

= - \frac{cos ( 2 θ - 10 )}{sin ( 2 θ - 10 )} + \frac{sin ( \frac{18 θ + 18 0 ^{\circ}}{18} )}{cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}

sin (- 10 + 2 θ), cos (\frac{18 0 ^{\circ} + θ 18}{18})

المضاعف المشترك الأصغر لـ:

sin (2 θ - 10) cos (\frac{18 θ + 18 0 ^{\circ}}{18})

sin (- 10 + 2 θ), cos (\frac{18 0 ^{\circ} + θ \cdot 18}{18})

Lowest Common Multiplier (LCM)

Compute an expression comprised of factors that appear either in

sin (- 10 + 2 θ)

cos (\frac{18 0 ^{\circ} + θ 18}{18})

= sin (2 θ - 10) cos (\frac{18 θ + 18 0 ^{\circ}}{18})

اكتب مجددًا الكسور بحيث يكون المقام مشترك

sin (2 θ - 10) cos (\frac{18 θ + 18 0 ^{\circ}}{18})

اضرب كل بسط ومقام بتعبير الذي يؤدّي إلى مقام مشترك

For

\frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} :

multiply the denominator and numerator by

cos (\frac{18 θ + 18 0 ^{\circ}}{18})

\frac{cos ( - 10 + 2 θ )}{sin ( - 10 + 2 θ )} = \frac{cos ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}{sin ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}

For

\frac{sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )} :

multiply the denominator and numerator by

sin (2 θ - 10)

\frac{sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} )} = \frac{sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} ) sin ( 2 θ - 10 )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} ) sin ( 2 θ - 10 )}

= - \frac{cos ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}{sin ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )} + \frac{sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} ) sin ( 2 θ - 10 )}{cos ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} ) sin ( 2 θ - 10 )}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- cos ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} ) + sin ( \frac{18 0 ^{\circ} + θ \cdot 18}{18} ) sin ( 2 θ - 10 )}{sin ( 2 θ - 10 ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}

= \frac{- cos ( - 10 + 2 θ ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} ) + sin ( \frac{18 0 ^{\circ} + 18 θ}{18} ) sin ( 2 θ - 10 )}{sin ( 2 θ - 10 ) cos ( \frac{18 θ + 18 0 ^{\circ}}{18} )}

\frac{- cos ( - 10 + 2 θ ) cos ( \frac{18 0 ^{\circ} + 18 θ}{18} ) + sin ( - 10 + 2 θ ) sin ( \frac{18 0 ^{\circ} + 18 θ}{18} )}{cos ( \frac{18 0 ^{\circ} + 18 θ}{18} ) sin ( - 10 + 2 θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (- 10 + 2 θ) cos (\frac{18 0 ^{\circ} + 18 θ}{18}) + sin (- 10 + 2 θ) sin (\frac{18 0 ^{\circ} + 18 θ}{18}) = 0

Rewrite using trig identities

- cos (- 10 + 2 θ) cos (\frac{18 0 ^{\circ} + 18 θ}{18}) + sin (- 10 + 2 θ) sin (\frac{18 0 ^{\circ} + 18 θ}{18})

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

:فعّل متطابقة الجمع لزوايا

- cos (s) cos (t) + sin (s) sin (t) = - cos (s + t)

= - cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18})

- cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18}) = 0

- 1

اقسم الطرفين على

- cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18}) = 0

- 1

اقسم الطرفين على

\frac{- cos ( - 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} )}{- 1} = \frac{0}{- 1}

بسّط

cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18}) = 0

cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18}) = 0

cos (- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18}) = 0 :

حلول عامّة لـ

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n, - 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n, - 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n

حلّ:

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n

انقل

10

إلى الجانب الأيمن

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n

للطرفين

10

أضف

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} + 10 = 9 0^{\circ} + 36 0^{\circ} n + 10

بسّط

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n + 10

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n + 10

18

اضرب الطرفين بـ

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 9 0^{\circ} + 36 0^{\circ} n + 10

18

اضرب الطرفين بـ

2 θ \cdot 18 + \frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18 = 9 0^{\circ} \cdot 18 + 36 0^{\circ} n \cdot 18 + 10 \cdot 18

بسّط

2 θ \cdot 18 + \frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18 = 9 0^{\circ} \cdot 18 + 36 0^{\circ} n \cdot 18 + 10 \cdot 18

2 θ \cdot 18

بسّط:

36 θ

2 θ \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 36 θ

\frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18

بسّط:

18 0^{\circ} + 18 θ

\frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{( 18 0 ^{\circ} + 18 θ ) \cdot 18}{18}

18 :

إلغ العوامل المشتركة

= 18 0^{\circ} + 18 θ

9 0^{\circ} \cdot 18

بسّط:

162 0^{\circ}

9 0^{\circ} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= 162 0^{\circ}

\frac{18}{2} = 9 :

اقسم الأعداد

= 162 0^{\circ}

36 0^{\circ} n \cdot 18

بسّط:

648 0^{\circ} n

36 0^{\circ} n \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 648 0^{\circ} n

10 \cdot 18

بسّط:

180

10 \cdot 18

10 \cdot 18 = 180 :

اضرب الأعداد

= 180

36 θ + 18 0^{\circ} + 18 θ = 162 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 162 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 162 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 162 0^{\circ} + 648 0^{\circ} n + 180

انقل

18 0^{\circ}

إلى الجانب الأيمن

54 θ + 18 0^{\circ} = 162 0^{\circ} + 648 0^{\circ} n + 180

من الطرفين

18 0^{\circ}

اطرح

54 θ + 18 0^{\circ} - 18 0^{\circ} = 162 0^{\circ} + 648 0^{\circ} n + 180 - 18 0^{\circ}

بسّط

54 θ = 144 0^{\circ} + 648 0^{\circ} n + 180

54 θ = 144 0^{\circ} + 648 0^{\circ} n + 180

54

اقسم الطرفين على

54 θ = 144 0^{\circ} + 648 0^{\circ} n + 180

54

اقسم الطرفين على

\frac{54 θ}{54} = 26.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

بسّط

\frac{54 θ}{54} = 26.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

\frac{54 θ}{54}

بسّط:

θ

\frac{54 θ}{54}

\frac{54}{54} = 1 :

اقسم الأعداد

= θ

26.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

بسّط:

26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

26.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

جمّع التعابير المتشابهة

= 26.66666 \dots^{\circ} + \frac{180}{54} + \frac{648 0 ^{\circ} n}{54}

26.66666 \dots^{\circ}

اختزل:

26.66666 \dots^{\circ}

26.66666 \dots^{\circ}

2 :

إلغ العوامل المشتركة

= 26.66666 \dots^{\circ}

= 26.66666 \dots^{\circ} + \frac{180}{54} + \frac{648 0 ^{\circ} n}{54}

\frac{180}{54}

اختزل:

\frac{10}{3}

\frac{180}{54}

18 :

إلغ العوامل المشتركة

= \frac{10}{3}

= 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{648 0 ^{\circ} n}{54}

\frac{648 0 ^{\circ} n}{54}

اختزل:

\frac{36 0 ^{\circ} n}{3}

\frac{648 0 ^{\circ} n}{54}

18 :

إلغ العوامل المشتركة

= \frac{36 0 ^{\circ} n}{3}

= 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n

حلّ:

θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n

انقل

10

إلى الجانب الأيمن

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n

للطرفين

10

أضف

- 10 + 2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} + 10 = 27 0^{\circ} + 36 0^{\circ} n + 10

بسّط

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n + 10

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n + 10

18

اضرب الطرفين بـ

2 θ + \frac{18 0 ^{\circ} + 18 θ}{18} = 27 0^{\circ} + 36 0^{\circ} n + 10

18

اضرب الطرفين بـ

2 θ \cdot 18 + \frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18 = 27 0^{\circ} \cdot 18 + 36 0^{\circ} n \cdot 18 + 10 \cdot 18

بسّط

2 θ \cdot 18 + \frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18 = 27 0^{\circ} \cdot 18 + 36 0^{\circ} n \cdot 18 + 10 \cdot 18

2 θ \cdot 18

بسّط:

36 θ

2 θ \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 36 θ

\frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18

بسّط:

18 0^{\circ} + 18 θ

\frac{18 0 ^{\circ} + 18 θ}{18} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{( 18 0 ^{\circ} + 18 θ ) \cdot 18}{18}

18 :

إلغ العوامل المشتركة

= 18 0^{\circ} + 18 θ

27 0^{\circ} \cdot 18

بسّط:

486 0^{\circ}

27 0^{\circ} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= 486 0^{\circ}

3 \cdot 18 = 54 :

اضرب الأعداد

= 486 0^{\circ}

\frac{54}{2} = 27 :

اقسم الأعداد

= 486 0^{\circ}

36 0^{\circ} n \cdot 18

بسّط:

648 0^{\circ} n

36 0^{\circ} n \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 648 0^{\circ} n

10 \cdot 18

بسّط:

180

10 \cdot 18

10 \cdot 18 = 180 :

اضرب الأعداد

= 180

36 θ + 18 0^{\circ} + 18 θ = 486 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 486 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 486 0^{\circ} + 648 0^{\circ} n + 180

54 θ + 18 0^{\circ} = 486 0^{\circ} + 648 0^{\circ} n + 180

انقل

18 0^{\circ}

إلى الجانب الأيمن

54 θ + 18 0^{\circ} = 486 0^{\circ} + 648 0^{\circ} n + 180

من الطرفين

18 0^{\circ}

اطرح

54 θ + 18 0^{\circ} - 18 0^{\circ} = 486 0^{\circ} + 648 0^{\circ} n + 180 - 18 0^{\circ}

بسّط

54 θ = 468 0^{\circ} + 648 0^{\circ} n + 180

54 θ = 468 0^{\circ} + 648 0^{\circ} n + 180

54

اقسم الطرفين على

54 θ = 468 0^{\circ} + 648 0^{\circ} n + 180

54

اقسم الطرفين على

\frac{54 θ}{54} = 86.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

بسّط

\frac{54 θ}{54} = 86.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

\frac{54 θ}{54}

بسّط:

θ

\frac{54 θ}{54}

\frac{54}{54} = 1 :

اقسم الأعداد

= θ

86.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

بسّط:

86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

86.66666 \dots^{\circ} + \frac{648 0 ^{\circ} n}{54} + \frac{180}{54}

جمّع التعابير المتشابهة

= 86.66666 \dots^{\circ} + \frac{180}{54} + \frac{648 0 ^{\circ} n}{54}

86.66666 \dots^{\circ}

اختزل:

86.66666 \dots^{\circ}

86.66666 \dots^{\circ}

2 :

إلغ العوامل المشتركة

= 86.66666 \dots^{\circ}

= 86.66666 \dots^{\circ} + \frac{180}{54} + \frac{648 0 ^{\circ} n}{54}

\frac{180}{54}

اختزل:

\frac{10}{3}

\frac{180}{54}

18 :

إلغ العوامل المشتركة

= \frac{10}{3}

= 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{648 0 ^{\circ} n}{54}

\frac{648 0 ^{\circ} n}{54}

اختزل:

\frac{36 0 ^{\circ} n}{3}

\frac{648 0 ^{\circ} n}{54}

18 :

إلغ العوامل المشتركة

= \frac{36 0 ^{\circ} n}{3}

= 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

θ = 26.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}, θ = 86.66666 \dots^{\circ} + \frac{10}{3} + \frac{36 0 ^{\circ} n}{3}

رسم

أمثلة شائعة

4sin^2(x)=5-2cos(x)

4 sin^{2} (x) = 5 - 2 cos (x)

sin(x+pi/6)=-1

sin (x + \frac{π}{6}) = - 1

sec(x)= 4/3

sec (x) = \frac{4}{3}

4cos(x)+3cos(x)=5

4 cos (x) + 3 cos (x) = 5

4sin(2x)tan(x)-tan(x)=0

4 sin (2 x) tan (x) - tan (x) = 0