If A = 60°, what is the value of:

$\frac{10 \sin \frac{A}{2}+8 \cos A}{7 \sin \frac{3 A}{2}-12 \cos A} ?$

9

$\frac{10 \sin \frac{A}{2}+8 \cos A}{7 \sin \frac{3 A}{2}-12 \cos A} $

A = 60°

10 sin \(\frac{A}{2}\) + 8 cosA

= 10 × sin 30° + 8 cos 60°

= 10 ×  \(\frac{1}{2}\) + 8× \(\frac{1}{2}\) = 9

&  7 sin \(\frac{3A}{2}\) - 12 cosA 

= 7 sin 90°  - 12 cos60°
= 7 - 12 × \(\frac{1}{2}\) = 1

 Now , $\frac{10 \sin \frac{A}{2}+8 \cos A}{7 \sin \frac{3 A}{2}-12 \cos A} $ = 9