(cotx) (cos^2x)=2cotx?

Question

Note: cos^2 x = (cosx)^2

The answer key says the solutions are (pi/2) and (3pi/2).

Can anyone explain how to solve this problem step by step?

Thanks!

Answer 1

equate to zero  .. . .

(cot x)(cos^2 x) - (2cot x) = 0

then factor completely

(cot x) (cos^2 x - 2) = 0

(cot x) (cos x - √2) (cos x + √2) = 0

then

either

cot x = 0

cos x = √2 ≈ 1.4

cos x = -√2

but cosine values cannot be outside -1 and 1

thus only cot x = 0 would yield solution

and the answers are .. . .. .

π/2 and 3π/2