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प्रश्न
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
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उत्तर
LHS = `cosA/(1 + sinA)`
RHS = secA - tanA
= `1/cosA - sinA/cosA = (1 - sinA)/cosA`
= `(1 - sinA)/cosA((1 + sinA)/(1 + sinA)) = ((1 - sin^2A)/(cosA(1 + sinA)))`
= `cos^2A/(cosA(1 + sinA)) = cosA/((1 + sinA) ` = LHS
LHS = RHS
`cos A/(1+sinA) = secA - tanA`
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