Question

${\left(\sin A+\sec A\right)}^2+{\left(\cos A+cosecA\right)}^2=$

Answer 1

Solution:

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

$(\sin A\cos A+1{)}^2/{\cos }^{2}A+(\sin A\cos A+1{)}^2{\sin }^{2}A$

$\Rightarrow (\sin A\cos A+1{)}^2[\frac{1}{{\cos }^{2}A}+\frac{1}{{\sin }^{2}A}]$

$\Rightarrow (\sin A\cos A+1{)}^2\left[\frac{{\sin }^{2}A+{\cos }^{2}A}{{\cos }^{2}A{\sin }^{2}A}\right]$

$\Rightarrow {\left(\frac{\sin A\cos A+1}{{\cos }^{2}A{\sin }^{2}A}\right)}^2$

$\Rightarrow (1+cosecA.\sec A{)}^2$