What is expand (3cos(x)-3sin(x))^2 ?

The solution to expand (3cos(x)-3sin(x))^2 is -9sin(2x)+9

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expand (3cos(x)-3sin(x))^2

expand

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

- 9 sin (2 x) + 9

Solution steps

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

Apply Perfect Square Formula:

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

(3 cos (x) - 3 sin (x))^{2} = (3 cos (x))^{2} - 2 \cdot 3 cos (x) \cdot 3 sin (x) + (3 sin (x))^{2}

= (3 cos (x))^{2} - 2 \cdot 3 cos (x) \cdot 3 sin (x) + (3 sin (x))^{2}

Simplify

(3 cos (x))^{2} - 2 \cdot 3 cos (x) \cdot 3 sin (x) + (3 sin (x))^{2} : 9 (- sin (2 x) + 1)

= 9 (- sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

9 (- sin (2 x) + 1) = 9 (- sin (2 x)) + 9 \cdot 1

= 9 (- sin (2 x)) + 9 \cdot 1

Simplify

9 (- sin (2 x)) + 9 \cdot 1 : - 9 sin (2 x) + 9

= - 9 sin (2 x) + 9

\frac{1}{2} (1 + lo g_{2} (3))

\frac{1}{s ( s - 2 ) ( s - 1 )}

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

\frac{- 8 n ^{2} - 8 n - 1}{( 2 n + 1 ) ^{2}}

\frac{1}{2 ( s + 3 ) ^{2}}

What is expand (3cos(x)-3sin(x))^2 ?
The solution to expand (3cos(x)-3sin(x))^2 is -9sin(2x)+9