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Question
Prove the following identities:
sec2 A + cosec2 A = sec2 A . cosec2 A
Solution
L.H.S. = sec2 A + cosec2 A
= `1/(cos^2A) + 1/(sin^2A)`
= `(sin^2A + cos^2A)/(cos^2A sin^2A)`
= `1/(cos^2A sin^2A)`
= sec2 A cosec2 A
= R.H.S. ...(∵ sin2 A + cos2 A = 1)
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