What is cos^4(θ)-sin^4(θ) ?

The solution to cos^4(θ)-sin^4(θ) is cos(2θ)

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simplify cos^4(θ)-sin^4(θ)

simplify

cos^{4} (θ) - sin^{4} (θ)

cos (2 θ)

Solution steps

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 (θ) + sin (θ)) (cos (θ) - sin (θ))

Expand

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

= cos^{2} (θ) - sin^{2} (θ)

Rewrite using trig identities

= cos (2 θ)

cot^{2} (x) - 1

\frac{1}{x ^{2} - 4}

2^{4 - 1}

\frac{2 b + 2 a}{2}

(u + 3)^{2}