Question

Solve cotx + 2cotxsinx = 0 for 0 degrees < or equal to x < or equal to 180 degrees

Answer 1

90°

Explanation:

Answer 2

Explanation:

cotx +2cotxsinx =0

cotx +2
`(cosx)/(sinx)`× sinx= 0

cotx +2 cosx= 0

`(cosx)/(sinx)`+ 2cosx= 0

`(cosx+ 2cosxsinx)/(sinx)` = 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=
`(-1)/(2)` i.e. x= 210° or 330°

As, 0° ≤x≤ 180° ∴ x= 90°