Question

How do you verify `tan(x/2) - cot (x/2) = -2 cot x`?

Answer 1

Verify: tan x/2 - cot x/2 = - 2cot x

Explanation:

call x/2 = t -> x = 2t

`(sin t/cos t) - (cos t/sin t) = (sin^2 t - cos^2 t)/(sin t.cos t) =`

=`(1 - 2cos^2 t)/((sin 2t)/2) = -(2cos 2t)/(sin 2t) = -2cot x`