Prove that tan²A+cot²A+2=sec²A cosec²A
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Posted by Neeraj Sharma 4 years, 9 months ago
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Sia ? 4 years, 9 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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