Question

If tan A+B= root 3 and A-B= 1/root 3, find the value of A and B

Answer 1

Hey mate !!

Here's your answer !!

We know that,

Tan 30 = 1 / √ 3

Tan 60 = √ 3

It is given that,

A + B =  √ 3

A - B = 1 / √ 3

Substituting √ 3 as 60, 1 / √ 3 as 30.

A + B = 60
A - B = 30

B gets cancelled. After that we get,

2A = 90

=> A = 90 / 2 = 45   -----( 1 )

Substituting them in value of A.

A + B = 60

45 + B = 60

=> B = 60 - 45 = 15

Hence A = 45, B = 15.

Hope my answer helps !!

Cheers !!

Answer 2

Howdy!!

your answer is ---
since , tan A+B = √3

=> tanA+B = tan60°. [since tan60°=√3]

=> A+B = 60 .....(1)

also, tanA-B = 1/√3

=> tan A-B = tan30° [since tan30°= 1/√3]

=> A-B = 30° .....(2)

now, adding equation (1)&(2),we get

2A = 90°

=> A = 90/2=45°

=> A = 45°

PUT THIS VALUE IN EQUATION (1),WE GET

45°+B = 60°

=>B = 60-45

=> B = 15°

HENCE, A = 45 AND B = 15°

HOPE IT HELP YOU