Question

Prove the identity
sinx(cotx + cosx tan x) = cos x + sin2 x

Answer 1

Distribute the sin(x)
The sin(x) cancels with the sin(x) from the cot(x)
The cos(x) term on the left cancels with the cos(x) term from the tan(x)

Answer 2

Since you want the answer to be in terms of cos and sin, you need to convert cot and tan in terms of sin and cos.

tan x = sin x/cos x
cot x = 1/tan x = 1/(sin x/cos x) = cos x/sin x

sin x(cos x/sin x + cos x(sin x/cos x) = cos x + sin x(sinx) = cos x + sin^2 x