Prove that tan A1 - tan2A2 - cot A1 - cot2A2 - sin A cos A

#160;LHS =tan A(1 + tan^2A)^2 + cot A(1 + cot^2A)^2 #160; #160; #160; #160; =tan A ^4A + Acosec ^4A #160; ......... #160; ...

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Trigonometric Identity- 2

Prove that ...

Question

Prove that $\frac{t a n A}{(1 + t a n^{2} A)^{2}} + \frac{c o t A}{(1 + c o t^{2} A)^{2}} = s i n A c o s A$

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\frac{tan A}{(1 + {tan}^{2} A)^{2}} + \frac{cot A}{(1 + {cot}^{2} A)^{2}} = sin A cos A

\frac{tan A}{(1 + {tan}^{2} A)^{2}} + \frac{cot A}{(1 + {cot}^{2} A)^{2}} = sin A cos A

\frac{c o s A}{1 - t a n A} + \frac{s i n A}{1 - c o t A} = s i n A + c o s A

Prove the following identities:

$\frac{t a n A}{(1 + t a n^{2} A)^{2}} + \frac{c o t A}{(1 + c o t^{2} A)^{2}} = s i n A c o s A$

cot A - tan A = \frac{2 {cos}^{2} A - 1}{sin A cos A}

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