Question

tan A+B=1 and tan A-B=1/√3 find A and B

Answer 1

Heya

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Tan A + B = Tan 45

Becoz Tan 45 = 1

A + B = 45.... Equation ( i )

Tan ( A - B ) = Tan 30

Becoz Tan 30 = 1/√3

A - B = 30... Equation ( ii )

Adding both the equations

2A = 75

A = 37.5° And B = 7.5°

Answer 2

tan (A+B) = 1 = tan 45°

so, tan(A+B) = tan 45°

hence, A + B = 45. -------------------(i)

now, tan (A-B) = 1/ ✓3 = tan 30°

so, tan (A-B) = tan 30°

hence, A - B = 30. --------------------(ii)

(i) + (ii), we get

A + B + A - B = 45 + 30

2A = 75

A = (38.5)°

putting value of A in (ii)

38.5 - B = 30

B = (8.5)°