If tan (A-B) = 1/root 3 and tan (A + B) = root 3 then find the value of A and B
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Answered by
2
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°
Answered by
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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