Question

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

• A. $\sec A+cosecA$
• B. $\sin A+cosA$
• C. $\tan A+\cot A$
• D. $\cos A+\sin A$

Answer 1

Answer: (A)

$\sec A+cosecA$

$sinA(1+tanA)+cosA(1+cotA)$

$\Rightarrow sinA\left(1+\frac{\sin A}{\cos A}\right)+cosA\left(1+\frac{\cos A}{\sin A}\right)$

$\Rightarrow \frac{\sin A}{\cos A}\left(\sin A+\cos A\right)+\frac{\cos A}{\sin A}\left(\sin A+\cos A\right)$

$\Rightarrow \left(\sin A+\cos A\right)\left[\frac{{\sin }^{2}A+{\cos }^{2}A}{\sin A\cdot \cos A}\right]$

$\Rightarrow \frac{\sin A}{\sin A\cdot \cos A}+\frac{\cos A}{\sin A\cdot \cos A}$

$\Rightarrow \sec A+cosecA$