Question

Prove

1+cos X/1-cos X = (csc X + cot X)squared

Answer 1

sort of like rationalizing radical expressions, multiply top and bottom by (1+cosX), giving

(1+cosX)^2
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(1-cos^2X

= (1+cosX)^2/sin^2X
= [(1+cosX)/sinX]^2
= (cscX + cotX)^2