Question

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Answer 1

EXPLANATION.

⇒ tan(A + B) = 1. - - - - - (1).

⇒ tan(A - B) = 1/√3. - - - - - (2).

A > B  and  0° < A + B ≤ 90°.

As we know that,

We can write equation as,

⇒ tan(A + B) = tan(45°). - - - - - (1).

⇒ tan(A - B) = tan(30°). - - - - - (2).

⇒ A + B = 45°. - - - - - (1).

⇒ A - B = 30°. - - - - - (2).

Adding equation (1) and (2), we get.

⇒ 2A = 75°.

⇒ A = 37.5°.

Put the value of A = 37.5° in equation (1), we get.

⇒ A + B = 45°.

⇒ 37.5° + B = 45°.

⇒ B = 45° - 37.5°.

⇒ B = 7.5°.

Values of A = 37.5°  and  B = 7.5°.

Answer 2

Given : Tan (A + B)  =1   and Tan (A - B)  = 1/√3

A > B  and  0° < A + B < 90°

To Find :  Value of A and B

Solution:

0° < A + B < 90°

Tan (A + B)  =1

-> Tan (A + B)  = Tan 45°

=> A + B = 45°

Tan (A - B)  = 1/√3

=> Tan (A - B)  = 30°

=> A - B = 30°

Adding Both

=> 2A = 75°

=>  A = 37.5°

and B = 7.5°

Correct Answer is  A = 37.5°  and B = 7.5°

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