Question

10. If tan(A - B) = 1/13 and tan (A + B) = V3, find A and B.​

Answer 1

Answer:

Given,

tan(A - B) = 1/√3

=> tan(A - B) = tan 30° (tan 30° = 1/√3)

=>A - B = 30° -----------(i)

And,

tan (A + B) = √3

=> tan (A + B) = tan 60°

=> A + B = 60 -----------(ii)

Now,

(i) +(ii) => A - B + A + B = 30° + 60°

=> 2A = 90

=> A= 90/2

=> A= 45

Putting A= 45 in (i) we have---

=> 45 - B = 30°

=> 45-30= B

=> B = 15

Therefore,

A= 45 and B = 15

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