Question

How do you solve `cos^3/sinx=cotx`?

Answer 1

All the solutions are x=0,`pi/2, pi, (3pi)/2, 2pi`

Write `cos^3 x= sinx cotx = cos x`

`(cos^3x -cosx)=0`

`cosx(cos^2x-1)=0`

For cos x=0, x=`pi/2, (3pi)/2`,

For `cos^2x`-1=0, cos x= 1, -1

For cos x=1, x=0, `2pi`

For cos x= -1, x= `pi`