What is the general solution for 2sin(x)tan(x)=-tan(x) ?

The general solution for 2sin(x)tan(x)=-tan(x) is x=pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(x)tan(x)=-tan(x)

2 sin (x) tan (x) = - tan (x)

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

Solution steps

2 sin (x) tan (x) = - tan (x)

Subtract

- tan (x)

from both sides

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

Factor

2 sin (x) tan (x) + tan (x) : tan (x) (2 sin (x) + 1)

tan (x) (2 sin (x) + 1) = 0

Solving each part separately

tan (x) = 0 or 2 sin (x) + 1 = 0

tan (x) = 0 : x = πn

2 sin (x) + 1 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

cos (2 x) cos (x) - sin (2 x) sin (x) = - \frac{3}{2}

sec (θ) = tan (θ) + cot (θ)

sec^{2} (x) = \frac{4}{3}, 0 \leq x \leq 2 π

3 tan (3 θ) - 1 = 0

2 tan (x) = sec (x)

What is the general solution for 2sin(x)tan(x)=-tan(x) ?
The general solution for 2sin(x)tan(x)=-tan(x) is x=pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin