Question

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 1

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°