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