Question

2sin^2x= sin^2x+sinxcosx/cotx

Answer 1

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

so

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

Then

sin²(x) + sin(x) cos(x) / cot(x) = sin²(x) + sin²(x) = 2 sin²(x)