Question

if tan(A+B)=root3, tan(A-B)=1/root3.find A and B.

Answer 1

Tan ( A + B) = √3 ---------- eq 1
Tan (A - B) = 1 / √3 --------- eq 2

By equation 1 and 2 we will get

A + B = 60°
A - B = 30°
–—————
2A = 30°
A = 15°

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Answer 2

tan(A+B) = ✓3
tan(A+B) = tan60°(by comparing)
A+B= 60° (because tan60° = ✓3)..........(1)


tan(A-B) = (1/✓3)

tan(A-B) = tan30° ( because tan30°=(1/√3)

A-B= 30° (by comparing from above)......(2)

Adding (2) and (1)

A= 45°

Subtracting (2) from (1)
B= 15°





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