Question

1/(tan A + cot A) = cos A sin A
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Answer 1

Question:

$\frac{1}{tan \: a + cot \: a} = cosa \: sina$

Answer:

Take L.H.S

$\implies \: \frac{1}{tan \: a + cot \: a} \\ \\ \implies \: \frac{1}{ \frac{sin \: a}{cos \: a} + \frac{cos \: a}{sin \: a} } \\ \\ \implies \: \frac{1}{ \frac{ {sin}^{2}a + {cos}^{2}a }{cos \: a \: sin \: a} } \\ \\ \because \: {cos}^{2}a + {sin}^{2}a = 1 \\ \\ \implies \: \frac{1}{ \frac{1}{cos \: a \: sin \: } } \\ \\ \implies \: cosa \: sina$

Hence L.H.S= R.H.S