Question

tanθ/2-1/(tanθ/2)=-2/tanθ

Answer 1

令a=θ/2
左边=tana-1/tana
=(tan²a-1)/tana
=1/[tana/(tan²a-1)]
=-2/[2tana/(1-tan²a)]
=-2/tan2a
=-2/tanθ=右边

Answer 2

tanθ/2-1/(tanθ/2)
=(tan²θ/2-1)/(tanθ/2)
=-2/[2tanθ/2/(1-tanθ²/2)]
=-2/tan(2θ/2)
=-2/tanθ