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Prove that tan²A+cot²A+2=sec²A cosec²A

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Prove that tan²A+cot²A+2=sec²A cosec²A

Posted by Neeraj Sharma 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

LHS {tex}= tan^2 A + cot^2 A + 2{/tex}
{tex}= sec^2 A - 1 + cosec^2 A - 1 + 2{/tex}
= sec² A + cosec² A
{tex}=\frac{1}{\cos ^{2} A}+\frac{1}{\sin ^{2} A}{/tex}
{tex}=\frac{\sin ^{2} A+\cos ^{2} A}{\cos ^{2} A \cdot \sin ^{2} A}{/tex}
{tex}=\frac{1}{\cos ^{2} A \cdot \sin ^{2} A}{/tex}
{tex}=\frac{1}{\cos ^{2} A} \times \frac{1}{\sin ^{2} A}{/tex}
= sec² A. cosec² A = RHS

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