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a)If A and B are acute angles such that tanA=1/2, tanB=1/3 and tan(A+B)=tanA+taB/1-tanAtanB, show that A+B=45 o . b)sinB = cos(B-45), where B and (B-45) are acute angles.Find the value of the angle B?

a)If A and B are acute angles such that tanA=1/2, tanB=1/3 and tan(A+B)=tanA+taB/1-tanAtanB,
show that A+B=45o.
b)sinB = cos(B-45), where B and (B-45) are acute angles.Find the value of the angle B?

Grade:10

1 Answers

Arun
25763 Points
2 years ago
I

Given that, tanA = 1/3

tanB = 1/2

tan (A+ B) = ( tanA + tanB) / (1 - tanA tanB)

= (1/3 +1/2) / (1- 1/3×1/2)

= (5/6) / ( 1- 1/6)

= (5/6)/(5/6)

tan (A+B) =1

 

Hence (A + B) = 45°

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