What is the general solution for 4tan(x)=2sec^2(x) ?

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

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4tan(x)=2sec^2(x)

4 tan (x) = 2 sec^{2} (x)

x = \frac{π}{4} + πn

Solution steps

4 tan (x) = 2 sec^{2} (x)

Subtract

2 sec^{2} (x)

from both sides

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

Rewrite using trig identities

- (1 + tan^{2} (x)) \cdot 2 + 4 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

sin (x) + cos (x) + cot (x) = csc (x)

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

cos (x) = \frac{3}{13}

3 tan^{3} (x) - 9 tan (x) = 0

cot (θ) = - 1, cos (θ), 9 0^{\circ} < θ < 18 0^{\circ}

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