Question

If tan (A-B) = 1/root 3 and tan (A + B) = root 3 then find the value of A and B​

Answer 1

1 ) tan ( A + B ) = √3

tan ( A + B ) = tan 60°

A + B = 60° -----( 1 )

2 ) tan ( A - B ) = 1

tan ( A - B ) = tan 45°

A - B = 45° -----( 2 )

Add equation ( 1 ) and ( 2 ) , we get

2A = 105°

A = 52.5°

Put A = 52.5° in equation ( 1 ) ,

52.5 + B = 60

B = 60 - 52.5

B = 7.5°

Answer 2

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tan(A-B) = 1/√3

=> tan(A-B) = tan 30°

.•. A-B = 30°

=> A = 30+B ---(i)

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tan(A+B) = √3

=> tan(A+B) = tan 60°

.•. A+B = 60

putting value of A from (i),

=> 30+B+B = 60

=> 30+2B = 60

=> 2B = 60-30

=> B = 30/2

=> B = 15°

From (i),

A = B + 30 = 15 + 30 = 45°

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Answer:

A = 45° B = 15°

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