Question 318408:
Answer by gsmani_iyer(201)   (Show Source):
You can put this solution on YOUR website!
Identity used in solving the problem: 1-(cos^2x)=(sin^2x)
sinx/(1+cosx)+ sinx/(1-cosx) = 2 cosec x. By taking out lcm of the denominators,
sinx(1-cosx) + sinx(1+cosx)/(1 - cos^2x)
= (sinx - sinx*cosx + sinx + sinx*cosx)/sin^2 x
= 2sinx / sin^2x i.e 2*(sinx)/(sin^2x) after cancelling,
= 2*1/sinx = 2 cosec x Answer.
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