What is 1-(sin(x)-cos(x))^2 ?

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

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simplify 1-(sin(x)-cos(x))^2

simplify

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

sin (2 x)

Solution steps

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

Simplify

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

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

Expand

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

= 1 + sin (2 x) - 1

Group like terms

= sin (2 x) + 1 - 1

Subtract the numbers:

1 - 1 = 0

= sin (2 x)

(2 y + 1)^{2}

x^{4} + 7 x^{2} + 10

x^{3} y^{6} - 216 y^{9}

\frac{\frac{x}{x - 1}}{\frac{x}{x - 1} - 1}

\frac{24}{- 8}