Question

The value of $(1+\cot A-\text{cosec}A)(1+\tan A+\sec A)$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0

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