What is the general solution for tan^2(x)-sec(x)=1 ?

The general solution for tan^2(x)-sec(x)=1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan^2(x)-sec(x)=1

tan^{2} (x) - sec (x) = 1

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

tan^{2} (x) - sec (x) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 2, sec (x) = - 1

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

sin (θ) = \frac{3}{2}

sin (6 π)

cos (2 5^{\circ})

csc (\frac{4 π}{3})

cos (3 θ) = 1

What is the general solution for tan^2(x)-sec(x)=1 ?
The general solution for tan^2(x)-sec(x)=1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin