What is the general solution for 2tan^2(x)-3sec(x)=0 ?

The general solution for 2tan^2(x)-3sec(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2tan^2(x)-3sec(x)=0

2 tan^{2} (x) - 3 sec (x) = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 tan^{2} (x) - 3 sec (x) = 0

Rewrite using trig identities

(- 1 + sec^{2} (x)) \cdot 2 - 3 sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - \frac{1}{2}

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - \frac{1}{2} :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

5 sin (x) tan (x) - 4 tan (x) = 0

5 cos (5 x) = 0

7 cos (x) - 7 sin (x) = 0

9 sin (x) cos (x) = 5 cos (x)

3 cos (x) sin (x) = - sin (x)

What is the general solution for 2tan^2(x)-3sec(x)=0 ?
The general solution for 2tan^2(x)-3sec(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin