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Question
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
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Solution
(1 + tan A + sec A) (1 + cot A – cosec A)
= 1 + cot A – cosec A + tan A + 1 – sec A + sec A + cosec A – cosec A sec A
= `2 + cosA/sinA + sinA/cosA - 1/(sinAcosA)`
= `2 + (cos^2A + sin^2A)/(sinAcosA) - 1/(sinAcosA)`
= `2 + 1/(sinAcosA) - 1/(sinAcosA)`
= 2
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