Question

Find the value of x, if 

sin 2x = sin 60° cos 30° – cos 60° sin 30°

(a) 20° 

(b) 15° 

(c) 30° 

(d) 45°

Answer 1

(b) 15°

sin 2x = \(\frac{\sqrt3}{2}\times\frac{\sqrt3}{2}-\frac12\times\frac12\)

= \(\frac34-\frac14 = \frac12\)

∴  sin 2x = \(\frac12\) = sin 30° ⇒ 2x = 30° ⇒ x = 15°.