What is the general solution for tan(θ)csc(θ)+2tan(θ)=0 ?

The general solution for tan(θ)csc(θ)+2tan(θ)=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(θ)csc(θ)+2tan(θ)=0

tan (θ) csc (θ) + 2 tan (θ) = 0

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

tan (θ) csc (θ) + 2 tan (θ) = 0

Factor

tan (θ) csc (θ) + 2 tan (θ) : tan (θ) (csc (θ) + 2)

tan (θ) (csc (θ) + 2) = 0

Solving each part separately

tan (θ) = 0 or csc (θ) + 2 = 0

tan (θ) = 0 : θ = πn

csc (θ) + 2 = 0 : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Since the equation is undefined for:

πn

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

250 = 88 sin (θ) + 242 cos (θ)

4 + 2 csc (\frac{θ}{2}) = 8

2 cos (3 x) = \frac{1}{2}, x = \frac{17 π}{4}

cos (θ) = sin (3 6^{\circ})

2 sec^{2} (x) = tan^{2} (x) + 2 sec (x) + 4

What is the general solution for tan(θ)csc(θ)+2tan(θ)=0 ?
The general solution for tan(θ)csc(θ)+2tan(θ)=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin