What is the general solution for tan^2(x)-sec(x)-1=0 ?

The general solution for tan^2(x)-sec(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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tan^2(x)-sec(x)-1=0

tan^{2} (x) - sec (x) - 1 = 0

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

Solution steps

tan^{2} (x) - sec (x) - 1 = 0

Rewrite using trig identities

- 2 - sec (x) + sec^{2} (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - 1

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

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

7 sin (x) cos (x) + 9 cos (x) = 0

2 cos (3 x) + 1 = 0

4 cos^{2} (x) - 3 = 0, 0 \leq x \leq 2 π

3 cos (x) + 3 = 2 sin^{2} (x)

- 4 cos (x) = - sin^{2} (x) + 1

What is the general solution for tan^2(x)-sec(x)-1=0 ?
The general solution for tan^2(x)-sec(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin