Solve, find all solutions for cot(x)cos(x)+cot(x)=0 in [0,2pi) ?

Answers- A.(pi/2, pi, 3pi/2) B.(pi/3, 2pi/3) C.(No solutions) or D. (pi/2, 3pi/2)

1 Answer
May 7, 2018

A. x=pi/2,(3pi)/2

Explanation:

First, factor out cot(x) as it appears in both terms:
cot(x)(cos(x)+1)=0 Next, use the zero-product property:
cot(x)=0 Cotangent is equal to (cos)/(sin), so cos(x)=0 will satisfy cot(x)=0. Using the unit circle, this occurs at pi/2 and (3pi)/2.
x=pi/2,(3pi)/2
The other factor is
cos(x)+1=0 Isolate the trigonometric function:
cos(x)=-1 Using the unit circle, this occurs at pi.
x=pi/2,pi,(3pi)/2
This answer corresponds to A.