For what value of θ (in degrees) is the following equation true ?
$sin 3θ cos θ - cos 3θ sin θ = \frac{1}{2}, 0 < θ < \frac{\pi}{2}$
Answer & explanation
Correct answer: option 4
$sin 3θ cos θ - cos 3θ sin θ = \frac{1}{2}$
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