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Question
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
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Solution
LHS = sec A(1 + sin A )( sec A - tan A)
= `1/cos A (1 + sin A) (1/cos A - sin A/cos A)`
= `1/cos A (1 + sin A) ((1 - sin A)/cos A)`
= `(1 - sin^2 A)/(cos^2 A) = (cos^2 A)/(cos^2 A)`
= 1
= RHS
Hence proved.
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