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Basic Trigonometric Identities

If tan A+B=√3...

Question

If and;

0° < A + B ≤ 90°, A > B find A and B.

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Solution

⇒

⇒ A + B = 60 … (1)

⇒ tan (A − B) = tan30

⇒ A − B = 30 … (2)

On adding both equations, we obtain

2A = 90

⇒ A = 45

From equation (1), we obtain

45 + B = 60

B = 15

Therefore, ∠A = 45° and ∠B = 15°

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tan (A + B) = \sqrt{3}

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