Find the solutions of the equation....

Question

Find the solutions of the equation that are in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

2 tan t + sec² t = 0

Answer 1

sec²t = tan²t + 1

 

2tant + tan²t + 1 = 0

tan²t + 2tant + 1 = 0

(tant + 1)² = 0

tant = -1     second and fourth quadrants

 

t = 3π/4

t = 7π/4