Question

please solve question no. 21

Answer 1

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

$= \sin^{2}A + 2\sin A\csc A + \csc^{2}A + \cos^{2}A + 2\cos A\sec A + \sec^{2}A$

$= \sin^{2}A + \cos^{2}A + 2\sin A.\frac{1}{\sin A} + 2\cos A.\frac{1}{\cos A} +  \csc^{2}A  + \sec^{2}A$

$= 1 + 2 + 2 + 1 + \cot^{2}A + 1 + \tan^{2}A$

$= \underline{\underline{7 + \tan^{2}A + \cot^{2}A}},$

as required.