Question

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

Answer 1

A = 30° and B = 60°
L.H.S.
= sin(A + B)
= sin(30° + 60°)
= sin90°
= 1
R.H.S.
= sinA cosB  cosA sinB
= sin30° x cos60° + cos30° x sin60°

= `(1)/(2) xx (1)/(2) + sqrt(3)/(2) xx sqrt(3)/(2)`

= `(1)/(4) + (3)/(4)`

= `(4)/(4)`
= 1
⇒ sin(A + B) = sinA cosB + cosA sinB.