Question

"Question39
If sin A = 60° and B= 30°, verify that : tan (A-B) = tanA-tanB / 1+ tan A tan B
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

Hey there! Thanks for the question!

Given,
A = 60° , B = 30°

To verify : tan(A - B) = tanA-tanB / 1 + tanA tanB.

Now,
tan( 60 - 30 ) = tan60 - tan30 / 1 + tan60° tan30°

We know that, tan30 = 1/√3 , tan60 = √3

tan30° = ( √3) - ( 1/√3) / 1 + ( √3) ( 1/√3)

1/√3 = ( 3 - 1 / √3 ) / 2

1/√3 = 2/√3 / ( 2 )

1/√3 = 1/√3

Both sides of the equation are equal!

Therefore, We proved and verified tan (A-B) = tanA-tanB / 1+ tan A tan B , for A = 60° , B = 30°

Answer 2

Hey mate !!

Here's the answer !!

Given :

A = 60° 

B = 30°

To verify :

Tan ( A - B ) = Tan A - Tan B / 1 + Tan A . Tan B

Proof :

Lets substitute the values of A and B in the equation to be verified.

= Tan ( 60 - 30 ) = Tan 60 - Tan 30 / 1 + Tan 60 . Tan 30

= Tan ( 30 ) = ( Tan 60 - Tan 30 ) / 1 + Tan 60 . Tan 30 -----( Eqn. 1 )

We know that,

Tan 30 = 1 / √ 3

Tan 60 = √ 3

Hence substitute the above formulas in equation 1. We get,

= ( 1 / √ 3 ) = ( √ 3 - 1 / √ 3 ) / 1 + √ 3 * 1 / √ 3

= ( 1 / √ 3 ) = ( 3 - 1 / √ 3 ) / 1 + 1

= ( 1 / √ 3 ) = 2 / √ 3 / 2

=> 1 / √ 3 = 2 / 2 √ 3

=> 1 / √ 3 = 1 / √ 3

Hence Verified !!

 LHS = RHS !!

Hope my answer helps you mate !!

Cheers !!