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

The general solution for sec^2(x)-2=tan^2(x) is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

No Solution for x \in R

Solution steps

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

Subtract

tan^{2} (x)

from both sides

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

Express with sin, cos

\frac{1 - sin ^{2} ( x ) - 2 cos ^{2} ( x )}{cos ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - sin^{2} (x) - 2 cos^{2} (x) = 0

Rewrite using trig identities

- cos^{2} (x) = 0

Divide both sides by

- 1

cos (x) = 0

General solutions for

cos (x) = 0

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

No Solution for x \in R

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

tan (θ) sin (θ) + sin (θ) = 0

tan (x) = 0.5

3 sin (x) = cos (x)

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

What is the general solution for sec^2(x)-2=tan^2(x) ?
The general solution for sec^2(x)-2=tan^2(x) is No Solution for x\in\mathbb{R}