Question

If A = 30° and B = 60°, verify that cos (A + B) = cos A cos B − sin A sin B

Answer 1

Given

`A = 30^@ and B = 60^@`

To verify:

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

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

Therefore,

`cos(30 +  60) = cos 90`

= 0

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

Therefore,

cosA cos B - sin A sin B = cos 30 cos 60 - sin 30 sin 60

`= sqrt3/2 xx 1/2 - 1/2 xx sqrt3/2`

= 0

Hence it is verfified that

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