use pythagorean identity and factor

Question

2 tan ² (t) - 3 sec (t) = 0

Answer 1

2 (sec² t - 1) - 3 sec t = 0

2 sec² t - 2 - 3 sec t = 0

2 sec² t - 3 sec t - 2 = 0

Now factor and solve by zero product rule