Question

tan(A+B-C)=1
sec(B+C-A)=2
Find value of A,B,C​

Answer 1

Answer:

Step-by-step explanation:

tan(x)=1, when x=π/4

Here our x = A+B-C, thus A+B-C = π/4 ( = 45°)

sec(x)=2, when x=π/3

In our case x = B+C-A, leaving us with B+C-A = π/3 ( = 60°)

Solving these two equations

A+B-C = π/4 ( = 45°) - say equation 1

B+C-A = π/3 ( = 60°) - say equation 2

C = A+B-45° from equation 1

Substitute this C value in equation 2:

B+(A+B-45°)-A=60°

and as you can observe, the A and -A will get cancelled, leaving us with

2B = 105°, which gives B = 52.5°

Substituting value of B in equation 1:

A+7.5°=C

We can have any set of A and C values satisfying the above equation.

Hope you understood!