Is cos(2A)=2cos^2(A)-1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(2A)=2cos^2(A)-1

prove

cos (2 A) = 2 cos^{2} (A) - 1

True

Solution steps

cos (2 A) = 2 cos^{2} (A) - 1

Manipulating left side

cos (2 A)

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= cos^{2} (A) - (1 - cos^{2} (A))

Simplify

cos^{2} (A) - (1 - cos^{2} (A)) : 2 cos^{2} (A) - 1

= 2 cos^{2} (A) - 1

We showed that the two sides could take the same form

\Rightarrow True

2 sin^{2} (3 x) = 1 - cos (6 x)

sec^{2} (x) - 1 = \frac{tan ( x )}{cot ( x )}

sec (θ) cos (θ) = 1

cot (θ) (cot (θ) + tan (θ)) = csc^{2} (θ)

cos (\frac{π}{2} + y) = - sin (y)