Question

Solve that:-
${\left(\sin A+\cos ecA\right)}^2+{\left(\cos A+\sec A\right)}^2=7+{\tan }^{2}A+{\cot }^{2}A$

Answer 1

$(sinA+cosecA{)}^2+(cosA+secA{)}^2=7+ta{n}^{2}A+co{t}^{2}A$

LHS $(sinA+cosecA{)}^2+(cosA+secA{)}^2$

$=si{n}^{2}A+cose{c}^{2}A+2+co{s}^{2}A+se{c}^{2}A+2$

$=5+se{c}^{2}A+cose{c}^{2}A$ $\{si{n}^{2}A+co{s}^{2}A=1\}$

$=7+se{c}^{2}A-1+cose{c}^{2}A-1$

$=7+ta{n}^{2}A+co{t}^{2}A$

$1+ta{n}^{2}A=se{c}^{2}A$

$1+co{t}^{2}A=cose{c}^{2}A$