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

The general solution for 3tan^2(x)-2=csc^2(x)-cot^2(x) is x= pi/4+pin,x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3tan^2(x)-2=csc^2(x)-cot^2(x)

3 tan^{2} (x) - 2 = csc^{2} (x) - cot^{2} (x)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

3 tan^{2} (x) - 2 = csc^{2} (x) - cot^{2} (x)

Subtract

csc^{2} (x) - cot^{2} (x)

from both sides

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

Rewrite using trig identities

- 3 + 3 tan^{2} (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = - 1

tan (x) = 1 : x = \frac{π}{4} + πn

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

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

sin (3 θ) = - \frac{3}{2}

x, arctan (\frac{y}{x}) = 0

cos (x) = - 1, 0 \leq x < 2 π

2 cos^{2} (x) - 3 sin (x) - 2 = 0

4 sin (x) cos^{2} (x) = cos (x)

What is the general solution for 3tan^2(x)-2=csc^2(x)-cot^2(x) ?
The general solution for 3tan^2(x)-2=csc^2(x)-cot^2(x) is x= pi/4+pin,x=(3pi)/4+pin