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

The general solution for sec^2(2x)-2tan(2x)=0 is x= pi/8+(pin)/2

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

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

x = \frac{π}{8} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

tan (2 x) = 1

tan (2 x) = 1 : x = \frac{π}{8} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}

x, d u = cos (4 x)

(\frac{sin ( θ )}{2 cos ( θ )}) - 1 = 0

2 \cdot cos^{2} (2 x) + 9 \cdot cos (4 x) = - 2.4214900000000 \dots

tan (- x) = tan (x)

6 sin (θ) = 6 sin (2 θ)

What is the general solution for sec^2(2x)-2tan(2x)=0 ?
The general solution for sec^2(2x)-2tan(2x)=0 is x= pi/8+(pin)/2