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

The solution to expand (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2 is 36sin^2(x)

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

expand

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

36 sin^{2} (x)

Solution steps

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

Expand

(- 3 sin (x) + 3 sin (3 x))^{2} : 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + (3 cos (x) - cos (3 x) \cdot 3)^{2}

Expand

(3 cos (x) - cos (3 x) \cdot 3)^{2} : 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

Simplify

9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x) : 36 sin^{2} (x)

= 36 sin^{2} (x)

\frac{2}{( e ^{x} - e ^{- x} ) ^{2}}

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

6 (7 d + \frac{1}{2})

\frac{sin ^{2} ( x )}{( 1 + cos ( x ) ) ^{2}}

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

What is expand (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2 ?
The solution to expand (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2 is 36sin^2(x)