Question

If $x,y,z$ are in $A.P$, then $\frac{\sin x-\sin z}{\cos z-\cos x}$ is equal to

• A. $\tan y$
• B. $\cot y$
• C. $\sin y$
• D. $\cos y$

Answer 1

Answer: (B)

$\frac{\sin x-\sin z}{\cos z-\cos x}=\frac{2\cos \left(\frac{x+z}{2}\right)\sin \left(\frac{x-z}{z}\right)}{2\sin \left(\frac{x+z}{z}\right)\sin \left(\frac{x-z}{z}\right)}$
$=\cot \left(\frac{x+z}{2}\right)=\cot (y)$