What is the general solution for sec^2(x)-4tan(x)=0 ?

The general solution for sec^2(x)-4tan(x)=0 is x=1.30899…+pin,x=0.26179…+pin

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

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

x = 1.30899 \dots + πn, x = 0.26179 \dots + πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 2 + 3, tan (x) = 2 - 3

tan (x) = 2 + 3 : x = arctan (2 + 3) + πn

tan (x) = 2 - 3 : x = arctan (2 - 3) + πn

Combine all the solutions

x = arctan (2 + 3) + πn, x = arctan (2 - 3) + πn

Show solutions in decimal form

x = 1.30899 \dots + πn, x = 0.26179 \dots + πn

3 sin (2 x) = 6 sin (x)

sin (x) = \frac{1}{3} \cdot cos (x)

2 sin^{2} (x) - 1 = cos (x), 0 \leq x \leq 2 π

x, cos (3 y) = tan (2 x)

x, cos (x) = - \frac{26}{26}

What is the general solution for sec^2(x)-4tan(x)=0 ?
The general solution for sec^2(x)-4tan(x)=0 is x=1.30899…+pin,x=0.26179…+pin