Can you solve for x? cot x sin x + cot x = 0? Thank you.

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Answer 1 · 2018-04-08T00:50:22

#x=pi/2+npi#

All terms share the cotangent in common. Factor it out.

#cotx(sinx+1)=0#

We must now solve the following:

#cotx=0#

#sinx+1=0#

Regarding #cotx=0:#

Since #cotx=cosx/sinx,# the cotangent will be zero wherever the cosine is zero; thus,

#x=pi/2+npi#, as cotangent has a period of #pi# (meaning all values of cotangent repeat every #pi# units).

#sinx+1=0:#

#sinx=-1#

#x=(3pi)/2+2npi#, as sine has a period of #2pi.#

In these cases, #n# represents any integer.

Well, the solution #x=pi/2+npi# already encompasses the case of #x=(3pi)/2+2npi#.

So, we can ignore the second solution as including it would be redundant.

#x=pi/2+npi#