Question

Find all solutions of each equation on the interval [0, 2pi)


(cos^3x)/(sinx )=cot x

Answer 1

Explanation:

(cos³x)/(sin x)=cot x

(cos³ x)/(sin x)=(cos x)/sin x

sin x≠0

x≠0,π,2π

cos³x-cos x=0

cos x(cos²x-1)=0

either cos x=0,x=π/2 ,3π/2

or

cos²x-1=0

2 cos²x=2

1+cos 2x=2

cos 2x=1=cos2nπ,n=0,1,2

2x=2nπ

x=nπ

x=0,π,2π

But x≠0,π,2π

so x=π/2,3π/2