Question

If sin (A - B) = sin A cos B – cos A sin B and cos (A - B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.

Answer 1

For finding the values of sin 15º and cos 15°, we can split 15° into two angles such that,15° = 45° - 30° or we also can split 15° as 15° = 60° - 45°

You can use either way, answer won't change. 

Formula to use for calculating this value is already given in the question,

sin(A - B) = sin A cos B - cos A sin B ..... (1) 

cos(A - B) = cos A cos B + sin A sin B ..... (2)

Put A = 60° and B = 45°

A - B = 15°

Now put the values in formula 1 and 2,

And,

Thus we have,