What is the general solution for sqrt(3)cos(θ)=-cos(θ)tan(θ) ?

The general solution for sqrt(3)cos(θ)=-cos(θ)tan(θ) is θ=(2pi)/3+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)cos(θ)=-cos(θ)tan(θ)

3 cos (θ) = - cos (θ) tan (θ)

θ = \frac{2 π}{3} + πn

Solution steps

3 cos (θ) = - cos (θ) tan (θ)

Subtract

- cos (θ) tan (θ)

from both sides

3 cos (θ) + cos (θ) tan (θ) = 0

Factor

3 cos (θ) + cos (θ) tan (θ) : cos (θ) (3 + tan (θ))

cos (θ) (3 + tan (θ)) = 0

Solving each part separately

cos (θ) = 0 or 3 + tan (θ) = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

3 + tan (θ) = 0 : θ = \frac{2 π}{3} + πn

Combine all the solutions

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

θ = \frac{2 π}{3} + πn

cos (2 x) = cos (x) - cos (3 0^{\circ}) [180]

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

- 13 a \cdot sin (2 x) - 13 b \cdot cos (2 x) = 0

3 + sin (x) = 2

1 - sin (A) cos (A) = (sin (A) - cos (A))^{2}

What is the general solution for sqrt(3)cos(θ)=-cos(θ)tan(θ) ?
The general solution for sqrt(3)cos(θ)=-cos(θ)tan(θ) is θ=(2pi)/3+pin