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

Given:

…… (1)

…… (2)

To find:

The values of and

In this problem we need to find and

Hence to get angle we need to choose the value of A and B such that

So If we choose and

Then we get,

Therefore by substituting and in equation (1)

We get,

Therefore,

…… (3)

Now we know that,

, ,

Now by substituting above values in equation (3)

We get,

Therefore,

…… (4)

Now by substituting and in equation (2)

We get,

Therefore,

…… (5)

Now we know that,

, ,

Now by substituting above values in equation (5)

We get,

Therefore,

…… (6)

Therefore from equation (4) and (6)