Is cos^4(θ)-sin^4(θ)=1-2sin^2(θ) ?

The answer to whether cos^4(θ)-sin^4(θ)=1-2sin^2(θ) is True

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prove cos^4(θ)-sin^4(θ)=1-2sin^2(θ)

prove

cos^{4} (θ) - sin^{4} (θ) = 1 - 2 sin^{2} (θ)

True

Solution steps

cos^{4} (θ) - sin^{4} (θ) = 1 - 2 sin^{2} (θ)

Manipulating left 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

= 1 - 2 sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot (x) sin (x) sec^{2} (x) = sec (x)

tan (2 x) = \frac{sin ( 2 x )}{cos ( 2 x )}

sin^{2} (x) + 4 cos^{2} (x) = 4 - 3 sin^{2} (x)

sin (a + b) = sin (a) cos (b) + cos (a) sin (b)

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

Is cos^4(θ)-sin^4(θ)=1-2sin^2(θ) ?
The answer to whether cos^4(θ)-sin^4(θ)=1-2sin^2(θ) is True