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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cos (4 u)

We showed that the two sides could take the same form

\Rightarrow True

tan (u) cot (u) - cos^{2} (u) = sin^{2} (u)

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

cos (2 θ) = 1 - 2 sin^{2} (θ)

sin (x) = 1 - cos (x)

\frac{cos ( θ )}{cot ( θ )} = sin (θ)

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