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Question
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
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Solution
L.H.S. = `1/(tan A + cot A)`
= `1/((sin A)/(cos A) + (cos A)/(sin A))`
= `1/((sin^2A + cos^2A)/(sin A cos A))`
= `1/(1/(sin A cos A))` ...(∵ sin2A + cos2A = 1)
= sin A cos A
= R.H.S.
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