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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (1 - cos (x) - sin (x)) (1 - cos (x) - sin (x))

Distribute parentheses

= 1 \cdot 1 + 1 \cdot (- cos (x)) + 1 \cdot (- sin (x)) - cos (x) \cdot 1 - cos (x) (- cos (x)) - cos (x) (- sin (x)) - sin (x) \cdot 1 - sin (x) (- cos (x)) - sin (x) (- sin (x))

Simplify

1 \cdot 1 + 1 \cdot (- cos (x)) + 1 \cdot (- sin (x)) - cos (x) \cdot 1 - cos (x) (- cos (x)) - cos (x) (- sin (x)) - sin (x) \cdot 1 - sin (x) (- cos (x)) - sin (x) (- sin (x)) : sin (2 x) - 2 cos (x) - 2 sin (x) + 2

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

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

\frac{x - 4}{2 ( x + 4 )}

\frac{e ^{- 2 s}}{s ( s ^{2} + 2 s + 4 )}

(3 x^{3} - x)^{2}

P (1, 7, - 5) Q (- 9, 1, - 5)

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