What is the general solution for 2arctan(xe^{0/2})= pi/2 ?

The general solution for 2arctan(xe^{0/2})= pi/2 is x=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2arctan(xe^{0/2})= pi/2

2 arctan (x e^{\frac{0}{2}}) = \frac{π}{2}

x = 1

Solution steps

2 arctan (x e^{\frac{0}{2}}) = \frac{π}{2}

Divide both sides by

2

2 arctan (x e^{\frac{0}{2}}) = \frac{π}{2}

Divide both sides by

2

\frac{2 arctan ( x e ^{\frac{0}{2}} )}{2} = \frac{\frac{π}{2}}{2}

Simplify

\frac{2 arctan ( x e ^{\frac{0}{2}} )}{2} = \frac{\frac{π}{2}}{2}

Simplify

\frac{2 arctan ( x e ^{\frac{0}{2}} )}{2} : arctan (x e^{\frac{0}{2}})

\frac{2 arctan ( x e ^{\frac{0}{2}} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= arctan (x e^{\frac{0}{2}})

Simplify

\frac{\frac{π}{2}}{2} : \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

arctan (x e^{\frac{0}{2}}) = \frac{π}{4}

arctan (x e^{\frac{0}{2}}) = \frac{π}{4}

arctan (x e^{\frac{0}{2}}) = \frac{π}{4}

Apply trig inverse properties

arctan (x e^{\frac{0}{2}}) = \frac{π}{4}

arctan (x) = a \Rightarrow x = tan (a)

x e^{\frac{0}{2}} = tan (\frac{π}{4})

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

x e^{\frac{0}{2}} = 1

x e^{\frac{0}{2}} = 1

Solve

x e^{\frac{0}{2}} = 1 : x = 1

x e^{\frac{0}{2}} = 1

Apply rule

\frac{0}{a} = 0, a \neq = 0

\frac{0}{2} = 0

e^{0} x = 1

Apply rule

a^{0} = 1, a \neq = 0

1 \cdot x = 1

Multiply:

x \cdot 1 = x

x = 1

x = 1

2 sin (x) cos (x) - 2 cos (x) = 0

x, 2 cos (x) - 2 = 0

cos (θ) = - \frac{4}{3}

cos (x) = \frac{2.16}{3.42}

2 cos^{2} (θ) - 3 sin (θ) - 3 = 0

What is the general solution for 2arctan(xe^{0/2})= pi/2 ?
The general solution for 2arctan(xe^{0/2})= pi/2 is x=1