verify sin(2x)=2cot(x)/1+cot^2(x)

Answer 1

2cotx / (1 + cot²x) = 2cotx / [1 + cos²x/sin²x]

= 2(cosx/sinx) / [(sin²x + cos²x) / sin²x]

= 2(cosx/sinx) / [1 / sin²x]

= 2(cosx/sinx)(sin²x / 1) = 2sinxcosx = sin(2x)