Is cos^2(x)-sin^2(x)=cos(2x) ?

The answer to whether cos^2(x)-sin^2(x)=cos(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^2(x)-sin^2(x)=cos(2x)

prove

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

True

Solution steps

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

Manipulating right side

cos (2 x)

Rewrite using trig identities

= cos (x) cos (x) - sin (x) sin (x)

Simplify

cos (x) cos (x) - sin (x) sin (x) : cos^{2} (x) - sin^{2} (x)

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (θ) (1 - cos^{2} (θ)) = tan^{2} (θ)

cos^{2} (θ) + tan^{2} (θ) cos^{2} (θ) = 1

1 - cos (x) = sin (x)

csc (x) - sin (x) = cot (x) \cdot cos (x)

sin^{4} (y) - cos^{4} (y) = 1 - 2 cos^{2} (y)

Is cos^2(x)-sin^2(x)=cos(2x) ?
The answer to whether cos^2(x)-sin^2(x)=cos(2x) is True