What is the general solution for cot(θ+1)csc(θ-1)=0 ?

The general solution for cot(θ+1)csc(θ-1)=0 is θ= pi/2+pin-1

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cot(θ+1)csc(θ-1)=0

cot (θ + 1) csc (θ - 1) = 0

θ = \frac{π}{2} + πn - 1

Degrees

θ = 32.70422 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cot (θ + 1) csc (θ - 1) = 0

Solving each part separately

cot (θ + 1) = 0 or csc (θ - 1) = 0

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

cot (θ + 1) = 0

General solutions for

cot (θ + 1) = 0

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

θ + 1 = \frac{π}{2} + πn

θ + 1 = \frac{π}{2} + πn

Solve

θ + 1 = \frac{π}{2} + πn : θ = \frac{π}{2} + πn - 1

θ + 1 = \frac{π}{2} + πn

Move

1

to the right side

θ + 1 = \frac{π}{2} + πn

Subtract

1

from both sides

θ + 1 - 1 = \frac{π}{2} + πn - 1

Simplify

θ = \frac{π}{2} + πn - 1

θ = \frac{π}{2} + πn - 1

θ = \frac{π}{2} + πn - 1

csc (θ - 1) = 0 :

No Solution

csc (θ - 1) = 0

csc (x) \leq - 1 or csc (x) \geq 1

No Solution

Combine all the solutions

θ = \frac{π}{2} + πn - 1

What is the general solution for cot(θ+1)csc(θ-1)=0 ?
The general solution for cot(θ+1)csc(θ-1)=0 is θ= pi/2+pin-1