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Question
If A = B = 60°, verify that cos (A − B) = cos A cos B + sin A sin B
Solution
Given
A = B = 60°......(1)
To verify:
cos (A − B) = cos A cos B + sin A sin B
Now consider the left-hand side of the expression to be verified in equation (2)
Therefore,
cos (A − B) = cos (60 - 60)
= cos 0
= 1
Now consider the right-hand side of the expression to be verified in equation (2)
Therefore,
`cosAcosB + sin A sin B = cosBcosB + sin B sin B`
`= cos^2B + sin^2 B`
= 1
Hence it is verified that, cos (A − B) = cos A cos B + sin A sin B
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