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

The general solution for tan^2(2x)-1=sec(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/2+pin

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

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

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{2} + πn

Solution steps

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

Subtract

sec (2 x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sec (2 x) = 2 : x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

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

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{2} + πn

- 1.92 = cos (x)

\frac{sin ^{2} ( x )}{4} = \frac{cos ^{2} ( x )}{2}

θ, 2 sin (θ) = tan (θ)

5 cot^{2} (x) + 8 cot (x) + 3 = 0

- 2 sin^{2} (x) - cos (x) + 3 = 0

What is the general solution for tan^2(2x)-1=sec(2x) ?
The general solution for tan^2(2x)-1=sec(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/2+pin