What is factor cos^6(θ)+sin^6(θ) ?

The solution to factor cos^6(θ)+sin^6(θ) is (cos^2(θ)+sin^2(θ))(cos^4(θ)-sin^2(θ)cos^2(θ)+sin^4(θ))

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factor cos^6(θ)+sin^6(θ)

factor

cos^{6} (θ) + sin^{6} (θ)

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

Solution steps

cos^{6} (θ) + sin^{6} (θ)

Rewrite

cos^{6} (θ) + sin^{6} (θ)

(cos^{2} (θ))^{3} + (sin^{2} (θ))^{3}

= (cos^{2} (θ))^{3} + (sin^{2} (θ))^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

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

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

cos^{4} (x) + 2 cos^{2} (x) + 1

(4 g h^{4} - 8 g + 14 h) + 7 g h

(- 4 + 43 i)^{20}

(x) - 1

\frac{d}{d t} ((x) (sin (k t)))

What is factor cos^6(θ)+sin^6(θ) ?
The solution to factor cos^6(θ)+sin^6(θ) is (cos^2(θ)+sin^2(θ))(cos^4(θ)-sin^2(θ)cos^2(θ)+sin^4(θ))