Is cos^2(a)-sin^2(a)=1-2sin^2(a) ?

The answer to whether cos^2(a)-sin^2(a)=1-2sin^2(a) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove cos^2(a)-sin^2(a)=1-2sin^2(a)

prove

cos^{2} (a) - sin^{2} (a) = 1 - 2 sin^{2} (a)

True

Solution steps

cos^{2} (a) - sin^{2} (a) = 1 - 2 sin^{2} (a)

Manipulating left side

cos^{2} (a) - sin^{2} (a)

Rewrite using trig identities

cos^{2} (a) - sin^{2} (a)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= 1 - sin^{2} (a) - sin^{2} (a)

Add similar elements:

- sin^{2} (a) - sin^{2} (a) = - 2 sin^{2} (a)

= 1 - 2 sin^{2} (a)

= 1 - 2 sin^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

Is cos^2(a)-sin^2(a)=1-2sin^2(a) ?
The answer to whether cos^2(a)-sin^2(a)=1-2sin^2(a) is True