Question

$\sin A(1+\tan A)+\cos A(1+\cot A)=\sec A+\csc A$.

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

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

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

$=\text{sec}A+\text{csc}A$

So the relation is $\text{True}$