Question

( sin 75 degrees - sin 15 degrees) /(cos 75 degrees + cos 15 degrees) = 1 / square root of 3.

Answer 1

$$\begin{gathered} \mathrm{LHS}=\frac{\sin 75-\sin 15}{\cos 75+\cos 15} \\ =\frac{2\cos \left({\displaystyle \frac{75+15}{2}}\right).\sin \left({\displaystyle \frac{75-15}{2}}\right)}{2\cos \left({\displaystyle \frac{75+15}{2}}\right).\cos \left({\displaystyle \frac{75-15}{2}}\right)} \\ =\frac{\cos 45.\sin 30}{\cos 45.\cos 30} \\ =\frac{\sin 30}{\cos 30} \\ =\tan 30 \\ =\frac{1}{\sqrt{3}} \\ =\mathrm{RHS} \end{gathered}$$