Is cos^2(2a)-sin^2(2a)=cos(4a) ?

The answer to whether cos^2(2a)-sin^2(2a)=cos(4a) is True

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prove cos^2(2a)-sin^2(2a)=cos(4a)

prove

cos^{2} (2 a) - sin^{2} (2 a) = cos (4 a)

True

Solution steps

cos^{2} (2 a) - sin^{2} (2 a) = cos (4 a)

Manipulating left side

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

Rewrite using trig identities

= cos (4 a)

We showed that the two sides could take the same form

\Rightarrow True

tan (2 x) - 2 cos (x) = 0

cos^{2} (a) cot^{2} (a) = cot^{2} (a) - cos^{2} (a)

cos (θ) = \frac{1}{2}

csc (2 x) = \frac{1}{sin ^{2} ( x ) - 1}

(1 + tan^{2} (α)) (1 - sin^{2} (α)) = 1

Is cos^2(2a)-sin^2(2a)=cos(4a) ?
The answer to whether cos^2(2a)-sin^2(2a)=cos(4a) is True