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
MAXIMILIAN C.
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#.

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