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If tan (A + B) = 1 and tan(A-B)=1/sqrt3 , 0° < A + B < 90°, A > B, then find the values of A and B. - Mathematics

Sum

If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.

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Solution

tan (A+B) = 1

⇒ tan(A+B) = tan 45°

⇒ A +B = 45° ..........(1)

tan(A-B)`=1/sqrt3`

⇒ tan (A-B)=tan 30°

⇒ A - B = 30 ......(2)

On adding (1) and (2), we obtain

2A = 75°

⇒ A = 37.5°

Putting the value of A in (1) we get

37.5° + B = 45°

⇒ B = 7.5°

Therefore,∠A = 37.5° and ∠B = 7.5°

Concept: Trigonometric Ratios of Some Special Angles
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