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

The general solution for tan(θ)=cot(θ) is θ= pi/4+pin,θ=(3pi)/4+pin

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tan(θ)=cot(θ)

tan (θ) = cot (θ)

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Solution steps

tan (θ) = cot (θ)

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 : θ = \frac{π}{4} + πn

cot (θ) = - 1 : θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

sin (x) = 0.2

cos (z) = 0

sin^{2} (x) - 4 sin (x) - 5 = 0

sin^{2} (x) = 1 + cos (x)

sec^{2} (θ) - 4 = 0

What is the general solution for tan(θ)=cot(θ) ?
The general solution for tan(θ)=cot(θ) is θ= pi/4+pin,θ=(3pi)/4+pin