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

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

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

simplify

(sin (x) - cos (x)) (sin (x) + cos (x))

- cos (2 x)

Solution steps

(sin (x) - cos (x)) (sin (x) + cos (x))

Expand

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

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

Rewrite using trig identities

= - cos (2 x)

\frac{( x ^{3} - x ^{2} - 17 x - 15 )}{( x - 5 )}

\frac{1}{2} \cdot 8 \cdot 15

64800

cos^{4} (θ) - sin^{4} (θ)

cot^{2} (x) - 1

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