Is 2cos^2(θ)-1=cos(2θ) ?

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

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prove 2cos^2(θ)-1=cos(2θ)

prove

2 cos^{2} (θ) - 1 = cos (2 θ)

True

Solution steps

2 cos^{2} (θ) - 1 = cos (2 θ)

Manipulating right side

cos (2 θ)

Rewrite using trig identities

= cos^{2} (θ) - sin^{2} (θ)

Use the Pythagorean identity:

cos^{2} (θ) + sin^{2} (θ) = 1

sin^{2} (θ) = 1 - cos^{2} (θ)

= cos^{2} (θ) - (1 - cos^{2} (θ))

Simplify

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

= 2 cos^{2} (θ) - 1

We showed that the two sides could take the same form

\Rightarrow True

cos (3 B) = cos (B) (cos^{2} (B) - 3 sin^{2} (B))

tan (2 x) = \frac{1}{1 - tan ( x )} - \frac{1}{1 + tan ( x )}

sin (θ + \frac{π}{2}) = cos (θ)

sin (2 x) = \frac{2 cot ( x )}{csc ^{2} ( x )}

(1 - cos (x)) (1 + sec (x)) = sec (x) - cos (x)