What is the general solution for 6tan^2(x)=5sec(x) ?

The general solution for 6tan^2(x)=5sec(x) is x=0.84106…+2pin,x=2pi-0.84106…+2pin

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6tan^2(x)=5sec(x)

6 tan^{2} (x) = 5 sec (x)

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Solution steps

6 tan^{2} (x) = 5 sec (x)

Subtract

5 sec (x)

from both sides

6 tan^{2} (x) - 5 sec (x) = 0

Rewrite using trig identities

(- 1 + sec^{2} (x)) \cdot 6 - 5 sec (x) = 0

Solve by substitution

sec (x) = \frac{3}{2}, sec (x) = - \frac{2}{3}

sec (x) = \frac{3}{2} : x = arcsec (\frac{3}{2}) + 2 πn, x = 2 π - arcsec (\frac{3}{2}) + 2 πn

sec (x) = - \frac{2}{3} :

No Solution

Combine all the solutions

x = arcsec (\frac{3}{2}) + 2 πn, x = 2 π - arcsec (\frac{3}{2}) + 2 πn

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

x, cos^{2} (x) = 0.5

sin (x) = 0.24, 0 \leq x < 2 π

sec^{2} (θ) cot (θ) = 8

4 + 5 sin (x) = 1

120 = 23 sin (\frac{π}{6} (x)) + 107

What is the general solution for 6tan^2(x)=5sec(x) ?
The general solution for 6tan^2(x)=5sec(x) is x=0.84106…+2pin,x=2pi-0.84106…+2pin