Question

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

Answer 1

Given

A = B = 60°......(1)

To verify:

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

Now consider the left-hand side of the expression to be verified in equation (2)

Therefore,

cos (A − B) = cos (60 - 60)

= cos 0

= 1

Now consider the right-hand side of the expression to be verified in equation (2)

Therefore,

`cosAcosB + sin A sin B = cosBcosB + sin B sin B`

`= cos^2B + sin^2 B`

= 1

Hence it is verified that, cos (A − B) = cos A cos B + sin A sin B