Is cos(2θ)=cos^4(θ)-sin^4(θ) ?

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

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prove cos(2θ)=cos^4(θ)-sin^4(θ)

prove

cos (2 θ) = cos^{4} (θ) - sin^{4} (θ)

True

Solution steps

cos (2 θ) = cos^{4} (θ) - sin^{4} (θ)

Manipulating right side

cos^{4} (θ) - sin^{4} (θ)

Factor

cos^{4} (θ) - sin^{4} (θ) : (cos^{2} (θ) + sin^{2} (θ)) (cos (θ) + sin (θ)) (cos (θ) - sin (θ))

= (cos (θ) + sin (θ)) (cos (θ) - sin (θ)) (cos^{2} (θ) + sin^{2} (θ))

Rewrite using trig identities

= cos (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 2 A )}{1 - cos ( 2 A )} = cot (A)

sin (6 x) = 2 sin (3 x) cos (3 x)

sin (4 x) = 4 sin (x) cos (x)

(1 + cot^{2} (θ)) tan^{2} (θ) = sec^{2} (θ)

sin (a) + cos (a) = \frac{1 + tan ( a )}{sec ( a )}

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