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

The solution to (sin(x)-cos(x))^2 is -sin(2x)+1

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

simplify

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

- sin (2 x) + 1

Solution steps

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

Expand

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

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

Rewrite using trig identities

= - sin (2 x) + 1

\frac{2 x ^{3} + 4 x ^{2} + 2 x}{6 x ^{3} - 6 x}

tan (x) cos (x)

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

\frac{tan ( x ) - cot ( x )}{tan ( x ) + cot ( x )}

8 x^{8} y^{3} z^{32}