Question

tan square A+cot square A +2 =sec^ 2 A.cosec^2 A

Answer 1

Step-by-step explanation:

$\tt LHS -$

$\tan ^2 A + \cot ^2 A +2$

$\dfrac{\sin^2A}{\cos ^2 A}+ \dfrac{\cos ^2 A}{\sin^2 A} +2$

$\dfrac{\sin^4A +\cos ^4 A+2\sin^2A \cos^2A}{\sin^2 A \cos^2A}$

$\dfrac{(\sin^2A+\cos^2A)^2}{\sin^2 A \cos^2A}$

$\dfrac{1}{\sin^2 A \cos^2A}$

$\tt RHS-$

$\sec ^2 A · \cosec^2A$

$\dfrac{1}{\cos ^2 A} · \dfrac{1}{\sin^2A}$

$\dfrac{1}{\sin^2A\cos ^2 A}$