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

Question

Use the chain rule using all steps possible

Answer 1

This looks like it should be a double-angle rule: sin(2x) = 2 sin x cos x

The double-angle rules derive from the sum formulas

sin (a + b) = sin a cos b + cos a sin b          and

cos (a + b) = cos a cos b - sin a sin b

by setting b = a

sin (2x) = sin (x + x)

            = sin x cos x + cos x sin x

            = 2 sin x cos x

The chain rule usually refers to tools in differential and integral calculus, but I can't see an interpretation of what you posted that requires the chain rule.

Answer 2

Do you want to solve it?

In [0, 2pi), sin(x) = 0 is a solution, which gives x = 0, pi

If sin(x) ≠ 0, dividing both sides by sin(x) leads to

cos(x) = 1/2

=> x = pi/3, 5pi/3

Answer: x = {0, pi/3, pi, 5pi/3}