(sin x)(cot x + cos x tan x) = cos x + sin^2x

Question

Prove the identity. 

Answer 1

Isabelle,

 

Don't let the cotangent & tangent scare you off.  Just change everything to Sines & Cosines and work through the math.

 

Remember that tan x = sin x / cos x    and  cot x = 1/ tan x  = cos x / sin x.

 

So:  (sin x) (cot x + cos x tan x) = sin x (cos x/ sin x + cos x sin x/ cos x)

                                                = ( cos x + sin ² x)

 

That proves this identity.