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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cos (4 x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (\frac{π}{4} + x) + sin (\frac{π}{4} - x) = 2 cos (x)

sin (x) cot (x) sec (x) = 1

cot^{2} (a) + 1 = \frac{1}{sin ^{2} ( a )}

sin (θ) sec (θ) cot (θ) = 1

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