Question

6. Given that sin 2x = 1 and cos y = 3 2 , then the value of x – y is A. 2  B. 6  C. 12  D. 15

Answer 1

Answer:

$x - y = \frac{\pi}{12}$

Explanation:

Firstly,

$\sin(2x) = 1$

$\sin(2x) = \sin( \frac{\pi}{2} )$

$x = \frac{\pi}{4}$

Secondly,

$\cos(y) = \frac{ \sqrt{3} }{2}$

$\cos(y) = \cos( \frac{\pi}{6} )$

$y = \frac{\pi}{6}$

So,

$x - y = \frac{\pi}{4} - \frac{\pi}{6}$

$x - y = \frac{3\pi - 2\pi}{12}$

$x - y = \frac{\pi}{12}$