Question

If $\tan A=2$, then find the value of $\sec A\sin A+{\tan }^{2}A-\text{cosec}A.\cos A=\frac{11}{m}.Findm$

Answer 1

$\sec A.\sin A+{\tan }^{2}A-\csc A.\cos A=\frac{5}{m}$

L.H.S.-

$\sec A.\sin A+{\tan }^{2}A-\csc A.\cos A$

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

$\Rightarrow =\tan A+{\tan }^{2}A-\cot A$

$\Rightarrow =\tan A+{\tan }^{2}A-\frac{1}{\tan A}$

$\Rightarrow =2+2^2-\frac{1}{2}$

$\Rightarrow =2+4-\frac{1}{2}$

$\Rightarrow =\frac{11}{2}$

R.H.S.-

$\frac{11}{m}$

Given that $L.H.S.=R.H.S.$

$\Rightarrow m=2$