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

The general solution for tan(θ)=cot(θ),0<= θ<2pi is θ= pi/4 ,θ=(5pi)/4 ,θ=(3pi)/4 ,θ=(7pi)/4

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tan(θ)=cot(θ),0<= θ<2pi

tan (θ) = cot (θ), 0 \leq θ < 2 π

θ = \frac{π}{4}, θ = \frac{5 π}{4}, θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

Solution steps

tan (θ) = cot (θ), 0 \leq θ < 2 π

Subtract

cot (θ)

from both sides

tan (θ) - cot (θ) = 0

Rewrite using trig identities

- cot (θ) + \frac{1}{cot ( θ )} = 0

Solve by substitution

cot (θ) = 1, cot (θ) = - 1

cot (θ) = 1, 0 \leq θ < 2 π : θ = \frac{π}{4}, θ = \frac{5 π}{4}

cot (θ) = - 1, 0 \leq θ < 2 π : θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

Combine all the solutions

θ = \frac{π}{4}, θ = \frac{5 π}{4}, θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

sec (θ) = 1.984

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

sin (2 θ) = 2 cos (θ)

30 = 30 cos (\frac{1}{4} (x - 5)) + 15

sec (x) sin^{2} (x) = sec (x)

What is the general solution for tan(θ)=cot(θ),0<= θ<2pi ?
The general solution for tan(θ)=cot(θ),0<= θ<2pi is θ= pi/4 ,θ=(5pi)/4 ,θ=(3pi)/4 ,θ=(7pi)/4