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Question
Prove that `(sec A)/(tan A + cot A) = sin A`.
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Solution
L.H.S. = `(sec A)/(tan A + cot A)`
= `(sec A)/((sin A)/(cos A) + (cos A)/(sin A))`
= `(sec A)/((sin^2A + cos^2A)/(cosA sinA))`
= `(sec A)/(1/(cosA sinA))` ...[∵ sin2A + cos2A = 1]
= sec A cos A sin A
= `1/(cos A) xx cos A sin A`
= sin A
= R.H.S.
∴ `(sec A)/(tan A + cot A) = sin A`
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