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

The general solution for sec^2(x)+tan(x)=1 is x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

\frac{1}{cot ^{2} ( x )} + \frac{1}{cot ( x )} = 0

Solve by substitution

cot (x) = - 1

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn

4 sin^{2} (θ) - 1 = 0

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

cos (x) = - sin (x)

4 cos^{2} (x) - 2 = 0

tan (3 x) = 3

What is the general solution for sec^2(x)+tan(x)=1 ?
The general solution for sec^2(x)+tan(x)=1 is x=(3pi)/4+pin