# Math trigonometric identities proving?

How to prove this true:

(1+cosx)/sinx = cot(x/2)

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- BrainardLv 74 years agoFavorite Answer
LHS = (1+cosx)/sinx

= [ 1 + (2cos^2(x/2) - 1)]/2sin(x/2)cos(x/2)

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

= cos(x/2)/cos(x/2) * cos(x/2)/sin(x/2)

= 1 * cos(x/2)/sin(x/2)

= cot(x/2)

= RHS

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