Step-by-step explanation:
cotx +2cotxsinx =0
cotx +2 [tex]\frac{cosx}{sinx}[/tex]× sinx= 0
cotx +2 cosx= 0
[tex]\frac{cosx}{sinx}[/tex]+ 2cosx= 0
[tex]\frac{cosx+ 2cosxsinx}{sinx}[/tex] = 0
cosx +2 cosxsinx= 0
cosx ×(1+ 2sinx)= 0
Hence, either cosx= 0 that is x= 90° or 270°
or 1+ 2sinx = 0 that is sinx= [tex]\frac{-1}{2}[/tex] i.e. x= 210° or 330°
As, 0° ≤x≤ 180° ∴ x= 90°
