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Question
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
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Solution
L.H.S. = (sec A – cos A) (sec A + cos A)
= sec2 A – cos2 A
= (1 + tan2 A) – (1 – sin2 A)
= sin2 A + tan2 A
= R.H.S.
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