Is 6sin((5pi)/6)=2+2sin((5pi)/6) ?

The answer to whether 6sin((5pi)/6)=2+2sin((5pi)/6) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove 6sin((5pi)/6)=2+2sin((5pi)/6)

prove

6 sin (\frac{5 π}{6}) = 2 + 2 sin (\frac{5 π}{6})

True

Solution steps

6 sin (\frac{5 π}{6}) = 2 + 2 sin (\frac{5 π}{6})

Manipulating left side

6 sin (\frac{5 π}{6})

Simplify

6 sin (\frac{5 π}{6}) : 3

6 sin (\frac{5 π}{6})

Simplify

sin (\frac{5 π}{6}) : \frac{1}{2}

sin (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= 6 \cdot \frac{1}{2}

Simplify

6 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3

= 3

= 3

Manipulating right side

2 + 2 sin (\frac{5 π}{6})

Simplify

2 + 2 sin (\frac{5 π}{6}) : 3

2 + 2 sin (\frac{5 π}{6})

2 sin (\frac{5 π}{6}) = 1

2 sin (\frac{5 π}{6})

Simplify

sin (\frac{5 π}{6}) : \frac{1}{2}

sin (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= 2 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{2}{2}

Cancel the common factor:

2

= 1

= 2 + 1

Simplify

= 3

= 3

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{0}{sin ( x ) cos ( x )} = 0

p ro v e \frac{sin ( x )}{1 - cos ( x )} = 1

p ro v e cos (\frac{π θ}{2}) = - 0.25

p ro v e cot (x) + \frac{1}{cot ( x )} = sin (x) cos (x)

p ro v e \frac{sin ( 2 a )}{1 - sin ^{2} ( a )} = 2 tan (a)

Is 6sin((5pi)/6)=2+2sin((5pi)/6) ?
The answer to whether 6sin((5pi)/6)=2+2sin((5pi)/6) is True