Question

If tan(A+B)= square root 3, tan(A-B) = 1/square root 3, 0< A + B <= 90, A > B find A and B

Answer 1

Answer:-

Given:

tan (A + B) = √3

"√3" can be written as tan 60°.

Hence,

tan (A + B) = tan 60°

On comparing both sides we get,

A + B = 60° -- equation (1)

Similarly,

tan (A - B) = tan 30°

→ A - B = 30° -- equation (2)

Adding equations (1) & (2) we get,

→ A + B + A - B = 60° + 30°

→ 2A = 90°

→ A = 90°/2

→ A = 45°

Substitute the value of "A" in equation (1)

→ A + B = 60°

→ 45° + B = 60°

→ B = 60° - 45°

→ B = 15°

Hence, the measures of A and B are 45° , 15°.

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