Answer:
Explanation:
Take the right side of the given expression:
(cotA - 1/ cotA + 1)^2
= (cot A - 1)^2 / (cotA + 1)^2
= (cot^2A + 1 - 2 cotA) / ( (cot^2A + 1 + 2 cotA)
Now cosec^2 A = 1 + cot^2A so we have:
= (cosec^2A - 2 cotA) / (cosec^2A + 2 cot A)
=( 1/ sin^2A) - 2cosA/sinA
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(1/ sin^2A ) + 2cosA/sinA
= (1 - 2 sinAcosA) / sin^2A
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(1 +2 sinAcosA) / sin^2A
= (1 - 2 sinAcosA) / (1 +2 sinAcosA)
Now 2 sinAcosA = sin2A so this simplifies to:
(1 - sin2A / (1 + sin2A).
Which is the left side of the original identity.