Question

If A = 30° B = 60° verify Sin (A + B) = Sin A Cos B + cos A sin B

Answer 1

Given

`A = 30^@ and 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 (30 + 60)

= sin 90

= 1

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

Therefore;

`sinA cosB + cosA sinB = sin 30^@ cos 60^@ + cos 30^@ sin 60^@`

`= 1/2 xx 1/2 + sqrt3/2 xx (sqrt3)/2`

`= (1 + 3)/4`

= 1

Hence it is verified that,

Sin (A + B) = Sin A Cos B + cos A sin B