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Question
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
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Solution
L.H.S. = `sqrt(sec^2A + cosec^2A)`
= `sqrt(1/cos^2A + 1/sin^2A)`
= `sqrt((sin^2A + cos^2A)/(sin^2Acos^2A)`
= `sqrt(1/(sin^2Acos^2A)`
= `sqrt(1/(sinAcosA))`
R.H.S. = tan A + cot A
= `sinA/cosA + cosA/sinA`
= `(sin^2A + cos^2A)/(sinAcosA)`
= `1/(sinAcosA)`
L.H.S. = R.H.S.
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