What is the general solution for 5tan^2(x)-9sec(x)+2=0 ?

The general solution for 5tan^2(x)-9sec(x)+2=0 is x=1.07121…+2pin,x=2pi-1.07121…+2pin

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5tan^2(x)-9sec(x)+2=0

5 tan^{2} (x) - 9 sec (x) + 2 = 0

x = 1.07121 \dots + 2 πn, x = 2 π - 1.07121 \dots + 2 πn

Solution steps

5 tan^{2} (x) - 9 sec (x) + 2 = 0

Rewrite using trig identities

- 3 + 5 sec^{2} (x) - 9 sec (x) = 0

Solve by substitution

sec (x) = \frac{9 + 141}{10}, sec (x) = \frac{9 - 141}{10}

sec (x) = \frac{9 + 141}{10} : x = arcsec (\frac{9 + 141}{10}) + 2 πn, x = 2 π - arcsec (\frac{9 + 141}{10}) + 2 πn

sec (x) = \frac{9 - 141}{10} :

No Solution

Combine all the solutions

x = arcsec (\frac{9 + 141}{10}) + 2 πn, x = 2 π - arcsec (\frac{9 + 141}{10}) + 2 πn

Show solutions in decimal form

x = 1.07121 \dots + 2 πn, x = 2 π - 1.07121 \dots + 2 πn

- sin (A) + 2 cos (A) sin (A) = 0

sin (2 θ) = - \frac{1}{2}, \forall 0 \leq θ < 2 π

t, 2 - 2 cosh (t - 2) = 0

3 tan (θ) = - 3, 0 \leq θ \leq 2 π

sin (x) = \frac{39}{62}

What is the general solution for 5tan^2(x)-9sec(x)+2=0 ?
The general solution for 5tan^2(x)-9sec(x)+2=0 is x=1.07121…+2pin,x=2pi-1.07121…+2pin