Question

please answer the question given in pic above ​

Answer 1

Step-by-step explanation:

sin (a + b - c) = 1/2

=> sin (a + b - c) = sin 30

=> a + b - c = 30 .............1

cos (b + c - a) = 1/2

=> cos (b + c - a) = cos 60

=> b + c - a = 60..............2

tan (c + a - b) = 1

=> tan (c + a - b) = tan 45

=> c + a - b = 45..............3

1 + 2

=> a + b - c = 30

-a + b + c = 60

=> 2b = 90 => b = 45

=> 1 + 3

=> a + b - c = 30

a - b + c = 45

=> 2a = 75 => a = 75/2

substituting values of b and a in equation 1, we get

75/2 + 45 + c = 30

=> 75 + 90 + 2c = 2×30 = 60

=> 165 + 2c = 60

=> 2c = 60 - 165 = -105

=> c = -105/2