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Question
If A = B = 60°. Verify `tan (A - B) = (tan A - tan B)/(1 + tan tan B)`
Solution
Given:
A = B = 60° ......(1)
To verify:
`tan (A - B) = (tan A - tanB)/(1 + tan Atan B)` ......(2)
Now consider LHS of the expression to be verified in equation (2)
Therefore.
`tan (A - B) = tan (B - B)`
= tan 0
= 0
Now consider RHS of the expression to be verified in equation (2)
Therefore
Now by substituting the value of A and B from equation (1) in the above expression
We get,
`(tan A - tan B)/(1 + tanA tan B) = (tan B - tan B)/(1 + tanB tan B)`
`= 0/(1 + tan^2 B)`
= 0
Hence it is verified that,
`tan (A - B) = (tan A - tan B)/(1 + tan tan B)`
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