find the solutions of the equation that are in the interval [0,2pi). cot^2 x - cot x = 0

Answer 1

Cot^2 x -Cot x =0 factor out Cot x from each term

Cot x(cot x -1) =0

Cot x =0 and Cot x =1 Remember cot is cos/sin

For Cot x =0 this will occur wherever cosine x is zero which is at pi/2 and 3pi/2 If sin=0 the function is undefined

For Cot x= 1 this will occur wherever sin equals cosine which is pi/4 and 5pi/4