Question

If $\text{cosec}({90}^0+A)+x\cot A\cot ({90}^0+A)=\sin ({90}^0+A)$, then find $x$.

Answer 1

$co\sec ({90}^0+A)+x\cot A({90}^0+A)=\sin ({90}^0+A)$
$\Rightarrow \sec A+x\cot A(-\tan A)=\cos A$
$\Rightarrow \sec A-x=\cos A$
$\Rightarrow \sec A-\cos A=\frac{1-{\cos }^{2}A}{\cos A}$
$\Rightarrow x=\frac{{\sin }^{2}A}{\cos A}=\tan A\sin A$