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Question
Prove the following identities:
(sec A – cos A) (cot A + tan A) = sec A tan A
Theorem
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Solution
LHS = `(1 / (cos A) - cos A)((cos A)/(sin A) + (sin A)/(cos A))`
= `((1 - cos^2A))/(cos A) xx ((cos^2A + sin^2A))/(sin A cos A)`
= `(sin^2A)/(sin A cos^2A)`
= `(sin A)/(cos^2A)`
= `(1/(cos A) xx (sin A)/(cos A))`
= (sec A tan A) = RHS
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