What is the general solution for 3tan(θ)-cot(θ)=5 ?

The general solution for 3tan(θ)-cot(θ)=5 is θ=2.96305…+pin,θ=1.07459…+pin

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3tan(θ)-cot(θ)=5

3 tan (θ) - cot (θ) = 5

θ = 2.96305 \dots + πn, θ = 1.07459 \dots + πn

Solution steps

3 tan (θ) - cot (θ) = 5

Subtract

5

from both sides

3 tan (θ) - cot (θ) - 5 = 0

Rewrite using trig identities

- 5 - cot (θ) + \frac{3}{cot ( θ )} = 0

Solve by substitution

cot (θ) = - \frac{5 + 37}{2}, cot (θ) = \frac{37 - 5}{2}

cot (θ) = - \frac{5 + 37}{2} : θ = arccot (- \frac{5 + 37}{2}) + πn

cot (θ) = \frac{37 - 5}{2} : θ = arccot (\frac{37 - 5}{2}) + πn

Combine all the solutions

θ = arccot (- \frac{5 + 37}{2}) + πn, θ = arccot (\frac{37 - 5}{2}) + πn

Show solutions in decimal form

θ = 2.96305 \dots + πn, θ = 1.07459 \dots + πn

cos (x) \cdot sin (x) = 1

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

sinh (x) = \frac{1}{2}

sin^{2} (x) \cdot sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

2 tan (θ) + sin (θ) cos (θ) = 0

What is the general solution for 3tan(θ)-cot(θ)=5 ?
The general solution for 3tan(θ)-cot(θ)=5 is θ=2.96305…+pin,θ=1.07459…+pin