What is the general solution for tan(θ)-2cos(θ)tan(θ)=0 ?

The general solution for tan(θ)-2cos(θ)tan(θ)=0 is θ=pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

Popular >

tan(θ)-2cos(θ)tan(θ)=0

tan (θ) - 2 cos (θ) tan (θ) = 0

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

Solution steps

tan (θ) - 2 cos (θ) tan (θ) = 0

Factor

tan (θ) - 2 cos (θ) tan (θ) : - tan (θ) (2 cos (θ) - 1)

- tan (θ) (2 cos (θ) - 1) = 0

Solving each part separately

tan (θ) = 0 or 2 cos (θ) - 1 = 0

tan (θ) = 0 : θ = πn

2 cos (θ) - 1 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

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

5 cos (x) = - 2 sin^{2} (x) + 4, 0 \leq x < 2 π

tan (x) = \frac{4 3}{4}

\frac{sin ^{2} ( x )}{1 - cos ( x )} = 1.23

x, 3 y = tan (6 x)

What is the general solution for tan(θ)-2cos(θ)tan(θ)=0 ?
The general solution for tan(θ)-2cos(θ)tan(θ)=0 is θ=pin,θ= pi/3+2pin,θ=(5pi)/3+2pin