If A = 60°, what is the value of:
$\frac{10 \sin \frac{A}{2}+8 \cos A}{7 \sin \frac{3 A}{2}-12 \cos A} ?$
Answer & explanation
Correct answer: option 3
$\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