Question

${\sec }^{2}A+cose{c}^{2}A={\sec }^{2}A\cdot cose{c}^{2}A$.

Answer 1

$se{c}^{2}A+cose{c}^{2}A=se{c}^{2}A.cose{c}^{2}A.$

=$\frac{1}{co{s}^{2}A}+\frac{1}{si{n}^{2}A}$

=$\frac{si{n}^{2}A+co{s}^{2}A}{co{s}^{2}Asi{n}^{2}A}$ = $\frac{1}{co{s}^{2}Asi{n}^{2}A}$

$=se{c}^{2}Acose{c}^{2}A=RHS$

Hence Proved