Question

State whether the following statement is true or false.

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

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{\sin x-\sin y}{\cos x+\cos y}$

Using transformation angle formula, we have

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

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

$=\tan \left(\frac{x-y}{2}\right)$

Hence the given statement is true.