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

The general solution for 0=2tan(x)-sec^2(x) is x= pi/4+pin

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

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

x = \frac{π}{4} + πn

Solution steps

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

Switch sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 1

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn

csc^{2} (x) + 6 csc (x) - 7 = 0

\frac{sin ( 2 x ) - 1}{3} = - \frac{1}{6}

2 sin^{2} (2 x) + cos (2 x) - 1 = 0

4 cos (x) + 2 = 3

sin (4 θ) = 4 sin (2 θ) cos (2 θ)

What is the general solution for 0=2tan(x)-sec^2(x) ?
The general solution for 0=2tan(x)-sec^2(x) is x= pi/4+pin