Question

1
If sin (A + B + C) = 1, tan (A
B)
and sec (A + C) = 2, then find the values of the angles A, B and C in degrees.​

Answer 1

the question is not clear, I am taking the question as below:

sin(A + B + C) = 1 = tan(A + B)

sec(A + C) = 2

now

sin(A + B + C) = 1 = sin 90°

A + B + C = 90°............(1)

tan !A + B,) = 1 = tan 45°

A + B = 45°........(2)

from (1) and (2)

C + 45° = 90°

C = 45°

now, sec (A + C) = 2 = sec 60°

A + C = 60°

A + 45° = 60°

A = 60° - 45°

A = 15°

B = 90° - (A + C)

= 90° - (15° + 45°)

= 90° - 60°

= 30°

thus, A = 15°, B = 30° , C = 45°