What is the general solution for csc^2(x)+3cot^2(x)=1 ?

The general solution for csc^2(x)+3cot^2(x)=1 is x= pi/2+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc^2(x)+3cot^2(x)=1

csc^{2} (x) + 3 cot^{2} (x) = 1

x = \frac{π}{2} + πn

Solution steps

csc^{2} (x) + 3 cot^{2} (x) = 1

Subtract

1

from both sides

csc^{2} (x) + 3 cot^{2} (x) - 1 = 0

Rewrite using trig identities

4 cot^{2} (x) = 0

Divide both sides by

4

cot (x) = 0

General solutions for

cot (x) = 0

x = \frac{π}{2} + πn

2 sin^{2} (θ) - sin (θ) - 3 = 0

4 sin (x) cos (x) + 1 = 0

4 sin (x) = 3 csc (x)

sin (2 θ) = \frac{3}{2}, 0 \leq θ < 2 π

- sin (4 x) = 0

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