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If a = B = 60°. Verify Tan (A - B) = (Tan a - Tan B)/(1 + Tan Tan B) - CBSE Class 10 - Mathematics

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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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Solution If a = B = 60°. Verify Tan (A - B) = (Tan a - Tan B)/(1 + Tan Tan B) Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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