What is the general solution for -sqrt(1+tan(x))=sec(x) ?

The general solution for -sqrt(1+tan(x))=sec(x) is x=pin,x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-sqrt(1+tan(x))=sec(x)

- 1 + tan (x) = sec (x)

x = πn, x = \frac{π}{4} + πn

Solution steps

- 1 + tan (x) = sec (x)

Square both sides

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

Subtract

sec^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 0, tan (x) = 1

tan (x) = 0 : x = πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = πn, x = \frac{π}{4} + πn

Verify solutions by plugging them into the original equation

x = πn, x = \frac{π}{4} + πn

sin (\frac{x}{2}) = sin (2 x)

cos (x) = cos (1)

sin^{2} (2 θ) = 0

y, x = 2 sec (y)

tan (π + c) = 1

What is the general solution for -sqrt(1+tan(x))=sec(x) ?
The general solution for -sqrt(1+tan(x))=sec(x) is x=pin,x= pi/4+pin