Question

If A, B and C are the acute angles such that sec (A + B - ©) = 2 and cot (A - B + C)=1/√3 then the measure of A is equal to​

Answer 1

Answer:

A = 60°

Step-by-step explanation:

sec (A + B - C) = 2

A + B + C = π

=> A + B = π - C

=> sec (π - C - C) = 2

=> sec (π - 2C) = 2

=> Cos(π - 2C) = 1/2

=> -Cos2C = 1/2

=>  Cos2C = -1/2

=> 2C = 120°

=> C = 60°

cot (A - B + C)=1/√3

=> Cot(π - 2B) = 1/√3

=> Tan(π - 2B) = √3

=>  -Tan2B = √3

=> Tan2B = -√3

=> 2B = 120°

=> B = 60°

A + B + C = 180°

=> A = 60°