What is the general solution for cot(θ)+tan(θ)=2 ?

The general solution for cot(θ)+tan(θ)=2 is θ= pi/4+pin

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cot(θ)+tan(θ)=2

cot (θ) + tan (θ) = 2

θ = \frac{π}{4} + πn

Solution steps

cot (θ) + tan (θ) = 2

Subtract

2

from both sides

cot (θ) + tan (θ) - 2 = 0

Rewrite using trig identities

- 2 + cot (θ) + \frac{1}{cot ( θ )} = 0

Solve by substitution

cot (θ) = 1

cot (θ) = 1 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn

3 cos^{2} (θ) - 1 = 0

sin (3 x - \frac{π}{6}) = - cos (3 x - \frac{π}{6})

cos^{2} (x) = \frac{1}{2} (1 + cos (x))

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

sin (3 x) cos (x) + cos (3 x) sin (x) = 1

What is the general solution for cot(θ)+tan(θ)=2 ?
The general solution for cot(θ)+tan(θ)=2 is θ= pi/4+pin