(cosecA - cotA)²= 1-cosA/1+cosA
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Step-by-step explanation:
Solving LHS,
(cosecA-cotA)^2
=Cosec^2A + cot^2A - 2cosecA.cotA
= 1/sin^2A + cos^2A/sin^2A - 2 cosA/sin^2A
=(1-cosA)^2 / sinA^2 [sin^2A + cos^2A=1]
=(1-cosA)^2 / (1-cosA^2)
[a^2-b^2=(a+b)(a-b)]
=(1-cosA)^2 / (1-cosA)(1+cosA)
=(1-cosA) / (1+cosA)= RHS
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