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

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

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

simplify

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

cos^{2} (2 x)

Solution steps

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

Simplify

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

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

Simplify

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

= (sin (2 x) + 1) (- sin (2 x) + 1)

Expand

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

= 1 - sin^{2} (2 x)

Use the Pythagorean identity:

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

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

= cos^{2} (2 x)

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

\frac{3.8 3 ^{2}}{3.1 3 ^{2}}

3^{2}

e^{- a t} H (t)

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