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प्रश्न
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
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उत्तर
LHS = `(1 + cosA)/(1 - cosA)`
= `(1 + 1/secA)/(1 - 1/secA) = (secA + 1)/(secA - 1)`
= `(secA + 1)/(secA - 1) . (secA - 1)/(secA - 1)`
= `(sec^2A - 1)/(secA - 1)^2 = tan^2A/(secA - 1)^2` (`Q sec^2A - 1 = tan^2A`)
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