Question

If A = B = 60°, verify `tan (A - B) = (tan A - tan B)/(1 + tan A tan B)`

Answer 1

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)`