if tan(A + B) = √3 and tan (A - B) = 1/√3 ; 0° <A+B≤90°; A >B, find A and B.
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Answer:
45° and 15°
Step-by-step explanation:
⇒ tan(A + B) = √3
⇒ tan(A + B) = tan60°
⇒ A + B = 60° ...(1)
⇒ tan(A - B) = 1/√3
⇒ tan(A - B) = tan30°
⇒ A - B = 30° ...(2)
Adding (1) and (2):
A + B = 60°
A - B = 30°
2A = 90°
A = 45°, therefore, B = 60° - 45° = 15°
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