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Question
If A = B = 60°, verify that sin (A − B) = sin A cos B − cos A sin B
Solution
Given:
A = 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 (B - B)`
= sin 0
= 0
Now by substituting the value of A and B from equation (1) in the above expression
We get,
`sinAcosB - cosAsinB = sin B cosB - cosBsinB`
= 0
Hence it is verified that,
sin (A − B) = sin A cos B − cos A sin B
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