Question

Verify 2sin(x)=cot(x)[cos(x)tan(x)+sin(x)]

Answer 1

cot(x) times tan(x) = 1

so, the first part would be just cosine x.

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

So, you have

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

which simplifies to

2sin(x)=2cos(x)

sin(x)=cos(x)

thus it's not an identity.

Answer 2

They are only equal at 45 degrees.