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