Cos2x-3cosx+1=cosecx÷cotx-cot2x then which of the following is true?

(1) x=(2n+1) π÷2 (2) x=2nπ

(3)x=2nπ+-cos inverse (2÷5) (4)no real x

Dear Student

cos2x−3cosx+1=cscx​/ (cotx−cot2x)

cotx−cot2x1​(−cotx+3cosxcotx−cos2xcotx+cot2x−3cosxcot2x+cos2xcot2x+cscx)=0


−2sin(π​/4−x/2​)sin(π​/4+x​/2)(2cosx−5)=0

⇒cosx=5​/2
or
sin(π​/4−x​/2)=0
or
sin(π​/4+x​/2)=0
⇒x=π​/2−2nπ,
x=2mπ+π​/2

Thanks