If sin(A + B + C) = 1, then tan(A - B) = 1/√3 and sec(A + C) = 2, f

1.	If sin(A + B + C) = 1, then tan(A - B) = 1/√3 and sec(A + C) = 2, find A, B and C respectively when they are acute.(A) 60°, 0°, 30°(B) 30°, 60°, 90°(C) 60°, 30°, 0°(D) 0°,60°, 30°
Answer» The correct option is: (C) 60°, 30°, 0° Explanation: We have, sin(A + B + C) = 1 => sin(A + B + C) = sin 90° => A + B + C = 90° ...(i) Also, tan(A - B) = 1/√3 = tan 30° => A - B = 30° ...(ii) and sec (A + C) = 2 = sec 60° => A + C = 60° ....(iii) From (ii) and (iii), we get B + C = 30° ...(iv) From (i) and (iv), we get, A = 60° . ^.. B = 30° [Using A = 60° in (ii)] and C = 0° [Using A = 60° in (iii)]

If sin(A + B + C) = 1, then tan(A - B) = 1/√3 and sec(A + C) = 2, find A, B and C respectively when they are acute.(A) 60°, 0°, 30°(B) 30°, 60°, 90°(C) 60°, 30°, 0°(D) 0°,60°, 30°

Answer»

The correct option is: (C) 60°, 30°, 0°

Explanation:

We have, sin(A + B + C) = 1

=> sin(A + B + C) = sin 90°

=> A + B + C = 90° ...(i)

Also, tan(A - B) = 1/√3 = tan 30°

=> A - B = 30° ...(ii)

and sec (A + C) = 2 = sec 60°

=> A + C = 60° ....(iii)

From (ii) and (iii), we get

B + C = 30° ...(iv)

From (i) and (iv), we get, A = 60°

. ^.. B = 30° [Using A = 60° in (ii)]

and C = 0° [Using A = 60° in (iii)]