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

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

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

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

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

Solution steps

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

Subtract

4 tan (x)

from both sides

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

x, 1 + sin (2 x - 3 0^{\circ}) = 0

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

\frac{cos ( - x )}{sin ( x )} = 0

5 sin (2 x) + 3 cos (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

cos (θ) = 0.6798, 0^{\circ} \leq θ \leq 36 0^{\circ}

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