What is the solution for c given that cot(4c - pi/4) + tan(2c + pi/4) = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the value of c such that cot(4c - pi/4) + tan(2c + pi/4) = 0

cot(4c - pi/4) + tan(2c + pi/4) = 0

=> cos(4c - pi/4)/sin(4c - pi/4) + sin(2c + pi/4)/cos(2c + pi/4) = 0

=> cos(4c - pi/4)cos(2c + pi/4) + sin(2c + pi/4)sin(4c - pi/4) = 0

=> cos(4c - pi/4 - 2c - pi/4) = 0

=> cos(2c - pi/2) = 0

=> sin 2c = 0

2c = 0 + n*2pi and 2c = pi + n*2pi

=> c = n*pi and c = pi/2 + n*pi

The values of c that satisfy the equation are n*pi and pi/2 + n*pi