help with variable multiplication and division please

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nhtw
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Report Thread starter 5 years ago
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I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
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Zacken
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(Original post by nhtw)
I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
Multiplying can give spurious solutions whilst dividing loses solutions (some times) \sin x = 1 precisely when \cos x = 0 so you're essentially dividing by zero.

You could also manipulate that into \tan x = \sec x after which a quick sketch demonstrates no solutions.
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Zacken
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(Original post by nhtw)
I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
P.S: you're not dividing or multiplying variables, you dividing and multiplying functions.
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