What is the general solution for (tan(θ))/(cot(θ))=1 ?

The general solution for (tan(θ))/(cot(θ))=1 is θ= pi/4+pin,θ=(3pi)/4+pin

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(tan(θ))/(cot(θ))=1

\frac{tan ( θ )}{cot ( θ )} = 1

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

Solution steps

\frac{tan ( θ )}{cot ( θ )} = 1

Subtract

1

from both sides

\frac{tan ( θ )}{cot ( θ )} - 1 = 0

Simplify

\frac{tan ( θ )}{cot ( θ )} - 1 : \frac{tan ( θ ) - cot ( θ )}{cot ( θ )}

\frac{tan ( θ ) - cot ( θ )}{cot ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

4 sin^{2} (x) = 4

tan (x) = \frac{- \frac{4}{3} 3}{- 4}

3 - 2 sin (θ) = - 3 + 2 sin (θ)

sin (x) - 0.75 = 0

2 cos^{2} (x) + cos (x) - 6 = 0

What is the general solution for (tan(θ))/(cot(θ))=1 ?
The general solution for (tan(θ))/(cot(θ))=1 is θ= pi/4+pin,θ=(3pi)/4+pin