Is cos(2x-pi/2)=cos(pi/2-2x) ?

The answer to whether cos(2x-pi/2)=cos(pi/2-2x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(2x-pi/2)=cos(pi/2-2x)

prove

cos (2 x - \frac{π}{2}) = cos (\frac{π}{2} - 2 x)

True

Solution steps

cos (2 x - \frac{π}{2}) = cos (\frac{π}{2} - 2 x)

Manipulating left side

cos (2 x - \frac{π}{2})

Use the negative angle identity:

cos (- x) = cos (x)

= cos (\frac{π}{2} - 2 x)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{π}{2} - x) cot (\frac{π}{2} + x) = - sin (x)

cos (x) \cdot csc (x) \cdot tan (x) = 1

- 2 sin (2 (x + 45)) = 2 cos (2 x)

cos^{2} (x) \frac{1}{cos ^{2} ( x )} = 1

(sin (\frac{4 π}{3})) = - \frac{3}{2}

Is cos(2x-pi/2)=cos(pi/2-2x) ?
The answer to whether cos(2x-pi/2)=cos(pi/2-2x) is True