Question

If three angles A,B,C are in A.P then the value of $\frac{\sin A-\sin C}{\cos C-\cos A}$ is equal to -

• A. $\cot \left(\frac{A-C}{2}\right)$
• B. $\cot B$
• C. $\tan B$
• D. None of these

Answer 1

The correct option is B $\cot B$

Given angles A,B,C are in A.P.

$2B=A+C$

Now, $\frac{\sin A-\sin C}{\cos C-\cos A}$
$=\frac{2\cos \frac{A+C}{2}\sin \frac{A-C}{2}}{2\sin \frac{A+C}{2}\sin \frac{A-C}{2}}$
$=\cot \frac{A+C}{2}$

$=\cot \frac{2B}{2}=\cot B$