If A, B, C are the acute angies, such that tan(A + B - C) = 1/(sqrt3) , cos(B + C - A) = 1/2 , and sin(C + A - B) = 1/(sqrt2) . The value of A + B + C will be equal to:

If A, B, C are the acute angies, such that tan(A + B - C)…

If A, B, C are the acute angies, such that tan(A + B - C) = $\frac{1}{\sqrt3}$ , cos(B + C - A) = $\frac{1}{2}$ , and sin(C + A - B) = $\frac{1}{\sqrt2}$ . The value of A + B + C will be equal to:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 135°.

tan (A + B - C) = 1/√3 = tan 30°

⇒ A + B - C = 30° .....(1)

cos (B + C - A) = 1/2 = cos 60°

⇒ B + C - A = 60° .....(2)

sin (C + A - B) = 1/√2 = sin 45°

⇒ C + A - B = 45° .....(3)

Adding equations (1), (2), and (3),

(A + B - C) + (B + C - A) + (C + A - B) = 30° + 60° + 45°

⇒ A + B + C = 135°

Hence, the required value is 135°.

SSC CHSL 2023 PYQ — Question 68