Double Angle Formulas

Question

Simplify:

tan x sin 2x

Answer 1

Since sin(2x) = 2sin(x)cos(x) then tan(x)sin(2x) = tan(x)2sin(x)cos(x). Now the trick is to write tan(x) = sin(x)/cos(x). So

tan(x)sin(2x) = sin(x)/cos(x) × 2 sin(x) cos(x)

Since the cos(x)'s cancel, we are left with

2sin ²(x)

Answer 2

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

tan(x) = sin(x) / cos(x)

2*sin(x)*cos(x) * sin(x) / cos(x) = 2*sin²(x)