What is the general solution for tan^2(x)+7=-10sec(x),0<x<2pi ?

The general solution for tan^2(x)+7=-10sec(x),0<x<2pi is x=1.67785…,x=-1.67785…+2pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan^2(x)+7=-10sec(x),0<x<2pi

tan^{2} (x) + 7 = - 10 sec (x), 0 < x < 2 π

x = 1.67785 \dots, x = - 1.67785 \dots + 2 π

Solution steps

tan^{2} (x) + 7 = - 10 sec (x), 0 < x < 2 π

Subtract

- 10 sec (x)

from both sides

tan^{2} (x) + 7 + 10 sec (x) = 0

Rewrite using trig identities

6 + sec^{2} (x) + 10 sec (x) = 0

Solve by substitution

sec (x) = - 5 + 19, sec (x) = - 5 - 19

sec (x) = - 5 + 19, 0 < x < 2 π :

No Solution

sec (x) = - 5 - 19, 0 < x < 2 π : x = arcsec (- 5 - 19), x = - arcsec (- 5 - 19) + 2 π

Combine all the solutions

x = arcsec (- 5 - 19), x = - arcsec (- 5 - 19) + 2 π

Show solutions in decimal form

x = 1.67785 \dots, x = - 1.67785 \dots + 2 π

tan (θ) = \frac{14}{11}

tan (3 φ - 4) = - \frac{1}{2}, 0 \leq φ \leq \frac{π}{2}

g, θ = arctan (\frac{5.54}{10 g} + 0.2)

tan (t) = \frac{3}{4}

2 cos (θ) - 2 sin (2 θ) = 0

What is the general solution for tan^2(x)+7=-10sec(x),0<x<2pi ?
The general solution for tan^2(x)+7=-10sec(x),0<x<2pi is x=1.67785…,x=-1.67785…+2pi