What is the general solution for 4cot^2(θ)-9=0 ?

The general solution for 4cot^2(θ)-9=0 is θ=0.58800…+pin,θ=2.55359…+pin

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4cot^2(θ)-9=0

4 cot^{2} (θ) - 9 = 0

θ = 0.58800 \dots + πn, θ = 2.55359 \dots + πn

Solution steps

4 cot^{2} (θ) - 9 = 0

Solve by substitution

cot (θ) = \frac{3}{2}, cot (θ) = - \frac{3}{2}

cot (θ) = \frac{3}{2} : θ = arccot (\frac{3}{2}) + πn

cot (θ) = - \frac{3}{2} : θ = arccot (- \frac{3}{2}) + πn

Combine all the solutions

θ = arccot (\frac{3}{2}) + πn, θ = arccot (- \frac{3}{2}) + πn

Show solutions in decimal form

θ = 0.58800 \dots + πn, θ = 2.55359 \dots + πn

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

2 cos^{3} (x) = cos (x)

3 sec (θ) + sec (θ) cot (θ) = 0

3 tan (\frac{x}{2}) - 1 = 0

cos (2 x) = 0.5

What is the general solution for 4cot^2(θ)-9=0 ?
The general solution for 4cot^2(θ)-9=0 is θ=0.58800…+pin,θ=2.55359…+pin