How do you find all solutions in the interval [0,2pi) of the equation #cos x = cot x#?

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How do you find all solutions in the interval [0,2pi) of the equation #cos x = cot x#?

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Answer 1 · 2016-04-07T04:48:33

#0, pi/2, (3pi)/2, 2pi#

Explanation:

f(x) = cos x - cot x = 0
#cos x - cos x/sin x = 0#
#cos^2 x - cos x = 0 # (condition: sin x different to zero)
#cos x( cos x - 1) = 0#
a. cos x = 0 --> #x = pi/2 and x = (3pi)/2#
b. cos x = 1 --> x = 0 and #x = 2pi#
Answer for #(0, 2pi):#
#0, pi/2, (3pi)/2, 2pi#

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How do you find all solutions in the interval [0,2pi) of the equation #cos x = cot x#?

1 Answer

Explanation:

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