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Prive that: tan /(1+ tan^2)^2 +cot/(1+cot^2)^2 …

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Prive that: tan /(1+ tan^2)^2 +cot/(1+cot^2)^2 =sin×cos

Posted by Vaibhav Bhardwaj 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

LHS {tex}=\frac{\tan A}{\left(1+\tan ^{2} A\right)^{2}}+\frac{\cot A}{\left(1+\cot ^{2} A\right)^{2}}{/tex}
{tex}=\frac{\tan A}{\left(\sec ^{2} A\right)^{2}}+\frac{\cot A}{\left(\ cosec ^{2} A\right)^{2}}{/tex}
{tex}=\frac{\sin A}{\cos A}{/tex} . cos⁴ A {tex}+\frac{\cos A}{\sin A}{/tex} . sin⁴ A
= sin A cos³ A + cos A sin³ A
= cos A sin A (cos² A + sin² A)
= sin A cos A = RHS

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