What is the general solution for 2+3cot^2(θ)-3csc(θ)=5 ?

The general solution for 2+3cot^2(θ)-3csc(θ)=5 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2+3cot^2(θ)-3csc(θ)=5

2 + 3 cot^{2} (θ) - 3 csc (θ) = 5

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Solution steps

2 + 3 cot^{2} (θ) - 3 csc (θ) = 5

Subtract

5

from both sides

3 cot^{2} (θ) - 3 csc (θ) - 3 = 0

Rewrite using trig identities

- 6 - 3 csc (θ) + 3 csc^{2} (θ) = 0

Solve by substitution

csc (θ) = 2, csc (θ) = - 1

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

csc (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{3 π}{2} + 2 πn

sinh (x) = 6

2 sin (6 x) + 2 sin (2 x) = 0

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

- 1.92 = cos (x)

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

What is the general solution for 2+3cot^2(θ)-3csc(θ)=5 ?
The general solution for 2+3cot^2(θ)-3csc(θ)=5 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ=(3pi)/2+2pin