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

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

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

prove

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

True

Solution steps

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

Manipulating right 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{cos ^{3} ( t )}{cot ^{2} ( t )} = sin^{2} (t) cos (t)

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

csc (θ) = \frac{cot ( θ )}{sec ( θ )} + sin (θ)

tan (x) sin (2 x) = 2 sin^{2} (x)

cos (x) tan (x) + sin (x) = 2 sin (x)

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