What is (sin(θ)+cos(θ))^2(sin(θ)-cos(θ))^2 ?

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

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simplify (sin(θ)+cos(θ))^2(sin(θ)-cos(θ))^2

simplify

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

cos^{2} (2 θ)

Solution steps

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

Simplify

(sin (θ) + cos (θ))^{2} : sin (2 θ) + 1

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

Simplify

(sin (θ) - cos (θ))^{2} : - sin (2 θ) + 1

= (sin (2 θ) + 1) (- sin (2 θ) + 1)

Expand

(1 + sin (2 θ)) (1 - sin (2 θ)) : 1 - sin^{2} (2 θ)

= 1 - sin^{2} (2 θ)

Use the Pythagorean identity:

1 = cos^{2} (2 θ) + sin^{2} (2 θ)

1 - sin^{2} (2 θ) = cos^{2} (2 θ)

= cos^{2} (2 θ)

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

v^{(- 2)} (2 v^{(4)} + 3 v^{(2)} - 2 v^{(- 3)})

e^{2 x} (e^{- 2 x})

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