What is the general solution for tan^2(θ)=3,0<= θ<= 2pi ?

The general solution for tan^2(θ)=3,0<= θ<= 2pi is θ= pi/3 ,θ=(4pi)/3 ,θ=(2pi)/3 ,θ=(5pi)/3

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tan^2(θ)=3,0<= θ<= 2pi

tan^{2} (θ) = 3, 0 \leq θ \leq 2 π

θ = \frac{π}{3}, θ = \frac{4 π}{3}, θ = \frac{2 π}{3}, θ = \frac{5 π}{3}

Solution steps

tan^{2} (θ) = 3, 0 \leq θ \leq 2 π

Solve by substitution

tan (θ) = 3, tan (θ) = - 3

tan (θ) = 3, 0 \leq θ \leq 2 π : θ = \frac{π}{3}, θ = \frac{4 π}{3}

tan (θ) = - 3, 0 \leq θ \leq 2 π : θ = \frac{2 π}{3}, θ = \frac{5 π}{3}

Combine all the solutions

θ = \frac{π}{3}, θ = \frac{4 π}{3}, θ = \frac{2 π}{3}, θ = \frac{5 π}{3}

3 sin (x) - 2 cos^{2} (x) = 0

4 cos^{2} (x) + 4 cos (x) - 3 = 0

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

2 sin (x) - (2 - 2) = 2 csc (x)

5 sin (62.83 x) = - 0.32

What is the general solution for tan^2(θ)=3,0<= θ<= 2pi ?
The general solution for tan^2(θ)=3,0<= θ<= 2pi is θ= pi/3 ,θ=(4pi)/3 ,θ=(2pi)/3 ,θ=(5pi)/3