Question

Solve : $(1+cotA-cosecA)(1+tanA+secA)=2$

Answer 1

$(1+\cot A-cosecA)(1+\tan A+\sec A)$

$\Rightarrow (1+\frac{\cos A}{\sin A}-\frac{1}{\sin A})(1+\frac{\sin A}{\cos A}+\frac{1}{\cos x})$

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

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

$\Rightarrow \frac{{\sin }^{2}A+{\cos }^{2}A+2\sin A\cos A-1}{\sin A\cos A}$

$\Rightarrow \frac{1+2\sin A\cos A-1}{\sin A\cos A}$ $({\sin }^{2}A+{\cos }^{2}A=1)$

$\Rightarrow \frac{2\sin A\cos A}{\sin A\cos A}$

$\Rightarrow 2$

$\Rightarrow$ RHS

$\therefore$ LHS$=$RHS.