What is the general solution for cot^2(θ)-4csc(θ)=-5 ?

The general solution for cot^2(θ)-4csc(θ)=-5 is θ= pi/6+2pin,θ=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot^2(θ)-4csc(θ)=-5

cot^{2} (θ) - 4 csc (θ) = - 5

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

cot^{2} (θ) - 4 csc (θ) = - 5

Subtract

- 5

from both sides

cot^{2} (θ) - 4 csc (θ) + 5 = 0

Rewrite using trig identities

4 + csc^{2} (θ) - 4 csc (θ) = 0

Solve by substitution

csc (θ) = 2

csc (θ) = 2 : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

tan (θ) = \frac{2}{7}

- 5 sin (3 x - π) = 0

tan (\frac{1}{2} x) = 0

2 cos (x) = - 2, 0 \leq x < 2 π

3 sec (x) csc (x) = 2 csc (x)

What is the general solution for cot^2(θ)-4csc(θ)=-5 ?
The general solution for cot^2(θ)-4csc(θ)=-5 is θ= pi/6+2pin,θ=(5pi)/6+2pin