Question

Evaluate: $\tan A\cot \left(\frac{A}{2}\right)-1$

• A. $\cos A$
• B. $\sin A$
• C. $\sec A$
• D. $cosecA$

Answer 1

Answer: (C)

$\sec A$

We know that $\cot \frac{A}{2}=\frac{1+\cos A}{\sin A}$

So, $\tan A\cot \frac{A}{2}-1\Rightarrow \frac{\sin A}{\cos A}.\frac{1+\cos A}{\sin A}-1\Rightarrow \sec A+1-1=\sec A$

Therefore, the answer is $\sec A$