Question

How do you verify `(1+cosx)/(1-cosx) - (1-cosx)/(1+cosx)=4cotxcscx`?

Answer 1

Verify trig expression.

Explanation:

Develop left side numerator:
`(1 + cos x)^2 - (1 - cos x)^2 = 4cos x`
Develop left side denominator:
`(1 - cos x)(1 + cos x) = (1 - cos^2 x) = sin^2 x.`
Full left side:
`(4cos x)/sin^2 x = 4(cos x/sin x) (1/sin x) = 4cot x.csc x`