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

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

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

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

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

Solution steps

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

Subtract

- 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 2, sec (x) = 0

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

sec (x) = 0 :

No Solution

Combine all the solutions

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

cos (2 θ) + 14 sin^{2} (θ) = 10

cos^{2} (x) - \frac{1}{4} = 0

3 (1 - sin (x)) = 2 cos^{2} (x)

∣ cos (x) ∣ = \frac{1}{2}

sin^{2} (θ) - cos^{2} (θ) = 0

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