Question

secant²∅+cosec²∅=secant²∅cosec²∅​

Answer 1

$\sf \: {sec}^{2} \theta + {cosec}^{2} \theta = {sec}^{2} \theta \: {cosec}^{2} \theta$

Now, we will use identify formula:

${\boxed{\sf{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta }}}} \\ \\ {\boxed{\sf{cosec}^{2} \theta = \frac{1}{ {sin}^{2} \theta}}}$

According to the question:

LHS

$\sf \implies \: \frac{1}{ {cos}^{2} \theta} + \frac{1}{ {sin}^{2} \theta} \\ \\ \sf \implies \: \frac{ {sin}^{2 } \theta + {cos}^{2} \theta }{ {sin}^{2} \theta {cos}^{2} \theta } \\ \\ \sf \implies \: \frac{1}{ {sin}^{2 } \theta {cos}^{2} \theta } \\ \\ \sf \implies \: {cosec}^{2} \theta {sec}^{2} \theta$

LHS = RHS

Hence, Proved.