For what value of θ (in degrees) is the following equation true ?

$sin 3θ cos θ - cos 3θ sin θ = \frac{1}{2}, 0 < θ < \frac{\pi}{2}$

15

$sin 3θ cos θ - cos 3θ sin θ = \frac{1}{2}$

Using ,

sin A . cos B - cosA . sinB = sin ( A - B )

Now,

sin 3θ cos θ - cos 3θ sin θ

= sin ( 3θ - θ )

= sin2θ 

ATQ,

sin2θ  = \(\frac{1}{2}\)

We know,

sin30º = \(\frac{1}{2}\)

So,

2θ = 30º

θ = 15º