Question

The number of solutions of the equation

|cotx| = cotx+$\frac { 1 } { \sin x }$ ( 0 ≤ x ≤2π) is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

1

Answer 2

If cotx > 0 , then $\frac { 1 } { \sin x }$ = 0 which is not possible.

Now if cotx < 0, then – cotx = cot x + $\frac { 1 } { \sin x }$

⇒ $\frac { 2 \cos x + 1 } { \sin x } = 0$ ⇒ cosx = -1/2

⇒ x = 2nπ ±$\frac { 2 \pi } { 3 }$ n ∈ I and 0 ≤ x ≤ 2π , also cot x < 0

⇒ x =$\frac { 2 \pi } { 3 }$.