What is the general solution for 7tan^2(θ)-4tan(θ)=0 ?

The general solution for 7tan^2(θ)-4tan(θ)=0 is θ=0.51914…+pin,θ=pin

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7tan^2(θ)-4tan(θ)=0

7 tan^{2} (θ) - 4 tan (θ) = 0

θ = 0.51914 \dots + πn, θ = πn

Solution steps

7 tan^{2} (θ) - 4 tan (θ) = 0

Solve by substitution

tan (θ) = \frac{4}{7}, tan (θ) = 0

tan (θ) = \frac{4}{7} : θ = arctan (\frac{4}{7}) + πn

tan (θ) = 0 : θ = πn

Combine all the solutions

θ = arctan (\frac{4}{7}) + πn, θ = πn

Show solutions in decimal form

θ = 0.51914 \dots + πn, θ = πn

tan (3 x) + 1 = sec (3 x)

- 2 sin^{2} (θ) + sin (θ) + 1 = 0

cot (θ) = \frac{1}{4}

3 sin (θ) cot (θ) - 2 sin (θ) = sin (θ)

4 - 7 sin^{2} (θ) = 3 cos^{2} (θ)

What is the general solution for 7tan^2(θ)-4tan(θ)=0 ?
The general solution for 7tan^2(θ)-4tan(θ)=0 is θ=0.51914…+pin,θ=pin