Show all steps to prove the following identity

Question

Sin 2x(tan x + cot x)= 2

Answer 1

sin2x = 2sinxcosx, tanx = sinx/cosx, cotx = cosx/sinx

sin2x(tanx+cotx)

=2sinxcosx(sinx/cosx + cosx/sinx)

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

=2(1)

= 2