Find the value of $x$ for which $(\sin A + \cosec A)^2 + (\cos A + \sec A)^2 = x + an^2 A + \cot^2 A$.

Question

Find the value of $x$ for which $(\sin A + \cosec A)^2 + (\cos A + \sec A)^2 = x + 	an^2 A + \cot^2 A$.

Accepted Answer

Step 1: $\sin^2 A + \cosec^2 A + 2 + \cos^2 A + \sec^2 A + 2 = x + 	an^2 A + \cot^2 A$
Step 2: $1 + (1 + \cot^2 A) + 2 + (1 + 	an^2 A) + 2 = x + 	an^2 A + \cot^2 A$
$7 + 	an^2 A + \cot^2 A = x + 	an^2 A + \cot^2 A$
Step 3: $	herefore x = 7$

Question

Solution