What is expand cos(5x)sin(x)+sin(5x)(-cos(x)+1) ?

The solution to expand cos(5x)sin(x)+sin(5x)(-cos(x)+1) is sin(5x)+sin(x-5x)

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expand cos(5x)sin(x)+sin(5x)(-cos(x)+1)

expand

cos (5 x) sin (x) + sin (5 x) (- cos (x) + 1)

sin (5 x) + sin (x - 5 x)

Solution steps

cos (5 x) sin (x) + sin (5 x) (- cos (x) + 1)

Expand

sin (5 x) (- cos (x) + 1) : - cos (x) sin (5 x) + sin (5 x)

= cos (5 x) sin (x) - cos (x) sin (5 x) + sin (5 x)

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (5 x) + sin (x - 5 x)

\frac{7 ( - y ^{2} + 49 )}{2}

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

(625 ln (5)) (x - 4) + 625

(x - \frac{2}{5})^{2}

- (t + \frac{1}{3}) e^{- 3 t} + C

What is expand cos(5x)sin(x)+sin(5x)(-cos(x)+1) ?
The solution to expand cos(5x)sin(x)+sin(5x)(-cos(x)+1) is sin(5x)+sin(x-5x)