Question

$\sin A(1+\tan A)+\cos A(1+\cot A)=\sec A+\text{cosec}A.$

• A. True
• B. False

Answer 1

The correct option is A True

$\sin A(1+\tan A)+\cos A(1+\cot A)$

$=\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$

$=\sin A+\frac{{\sin }^{2}A}{\cos A}+\cos A+\frac{{\cos }^{2}A}{\sin A}$

$=\frac{{\sin }^{2}A+{\cos }^{2}A}{\sin A}+\frac{{\sin }^{2}A+{\cos }^{2}A}{\cos A}$

$=\sec A+cosecA$