Why Do Additional Solutions Appear in Trigonometric Equations?

[Veronica_Oles]

Homework Statement

Solve cotxcsc²x=2cotx

Homework Equations

The Attempt at a Solution

cotx(csc²-2)

cotx = 0
x = no solution

x = sin^-1(1/√2)

or

x = sin^-1(-1/√2)

I come up with the solutions x = { π/4, 3π/4, 5π/4, 7π/4}

However the solutions are telling me that x can also be equal to π/2 and 3π/2 although I have no idea how this could be?

 

[eys_physics]

cotx = 0
x = no solution

This is wrong. What is the value of $\cot(\pi/2)$?

 

[Ray Vickson]

Homework Statement

Solve cotxcsc²x=2cotx

Homework Equations

The Attempt at a Solution

cotx(csc²-2)

cotx = 0
x = no solution

x = sin^-1(1/√2)

or

x = sin^-1(-1/√2)

I come up with the solutions x = { π/4, 3π/4, 5π/4, 7π/4}

However the solutions are telling me that x can also be equal to π/2 and 3π/2 although I have no idea how this could be?

Your understanding of the function $\cot x$ is faulty; plot the graph $y = \cot x$ for $0 \leq x \leq 2 \pi$ to see what happens at various values of $x$.