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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^2"A" + cos^2"A")/(cos"A" sin"A"))`
= `sec"A"/(1/(cos"A" sin"A"))` ......[∵ 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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