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

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

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

expand

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

- sin (2 x) + 1

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

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

= - sin (2 x) + 1

\frac{1}{π ( a ^{2} - b ^{2} )} + \frac{4 b \cdot c}{π ( a ^{4} - b ^{4} )}

(1.02)^{3}

\frac{( 2 - x ) ^{3}}{6}

a (- 5, 2) b (4, - 3)

\frac{1 + 3 x + x ^{2}}{( x - 19 ) ( x - 2 ) ( x + 6 )}

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