What is expand (8+(8+16cos(x)))/2 (8sin(x)) ?

The solution to expand (8+(8+16cos(x)))/2 (8sin(x)) is 32sin(2x)+64sin(x)

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expand (8+(8+16cos(x)))/2 (8sin(x))

expand

\frac{8 + ( 8 + 16 cos ( x ) )}{2} (8 sin (x))

32 sin (2 x) + 64 sin (x)

Solution steps

\frac{8 + ( 8 + 16 cos ( x ) )}{2} (8 sin (x))

Remove parentheses:

(a) = a

= \frac{8 + 8 + 16 cos ( x )}{2} \cdot 8 sin (x)

\frac{8 + 8 + 16 cos ( x )}{2} = 8 cos (x) + 8

= 8 sin (x) (8 cos (x) + 8)

= 8 sin (x) (8 cos (x) + 8)

Apply the distributive law:

a (b + c) = ab + a c

a = 8 sin (x), b = 8 cos (x), c = 8

= 8 sin (x) \cdot 8 cos (x) + 8 sin (x) \cdot 8

= 8 \cdot 8 sin (x) cos (x) + 8 \cdot 8 sin (x)

Multiply the numbers:

8 \cdot 8 = 64

= 64 sin (x) cos (x) + 64 sin (x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= 64 \cdot \frac{sin ( 2 x )}{2}

Simplify

64 \cdot \frac{sin ( 2 x )}{2} : 32 sin (2 x)

= 32 sin (2 x) + 64 sin (x)

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What is expand (8+(8+16cos(x)))/2 (8sin(x)) ?
The solution to expand (8+(8+16cos(x)))/2 (8sin(x)) is 32sin(2x)+64sin(x)