Question

If A = B = 60°, verify that sin (A − B) = sin A cos B − cos A sin B

Answer 1

Given:

A = B = 60°  .....(1)

To verify:

sin (A − B) = sin A cos B − cos A sin B  ......(2)

Now consider LHS of the expression to be verified in equation (2)

Therefore,

`sin (A - B) = sin (B - B)`

= sin 0

= 0

Now by substituting the value of A and B from equation (1) in the above expression

We get,

`sinAcosB - cosAsinB = sin B cosB - cosBsinB`

= 0

Hence it is verified that,

sin (A − B) = sin A cos B − cos A sin B