Question

Tan(a+b)=1/root3 and tan(a-b)=root 3 find the value of a and b

Answer 1

Answer:

A = 45° , B = -15°

Step-by-step explanation:

Given ---> tan ( A + B ) = 1 / √3 , tan ( A - B ) = √3

To find---> Value of A and B

Solution---> ATQ,

tan ( A + B ) = 1 / √3

=> tan ( A + B ) = tan 30°

=> A + B = 30° .......................( 1 )

ATQ, tan ( A - B ) = √3

=> tan ( A - B ) = tan 60°

=> A - B = 60° ..................... ( 2 )

Now we solve equation ( 1 ) and ( 2 ) by substitution method,

A - B = 60°

=> A = 60° + B

Putting A = ( 60° + B ) in equation ( 1 )

=> 60° + B + B = 30°

=> 2 B = 30° - 60°

=> 2 B = - 30°

=> B = - 15°

A + B = 30°

=> A - 15° = 30°

=> A = 30° + 15°

=> A = 45°