Find the value of a and of b .

Hence or otherwise, solve the equation $6\sin x\cos x = \frac{3}{2}$ , for $\frac{\pi }{4} \le x \le \frac{\pi }{2}$ .

recognizing double angle     M1

e.g. $3 \times 2\sin x\cos x$ , $3\sin 2x$

$a = 3$ , $b = 2$     A1A1     N3

[3 marks]

substitution $3\sin 2x = \frac{3}{2}$     M1

$\sin 2x = \frac{1}{2}$     A1

finding the angle     A1

e.g. $\frac{\pi }{6}$ , $2x = \frac{{5\pi }}{6}$

$x = \frac{{5\pi }}{{12}}$     A1     N2

Note: Award A0 if other values are included.

[4 marks]