Doesn’t multiplying both sides by sin x lose a solution? When I cross multiplied I also got a solution of x=90

(edited 1 month ago)

Original post by Gcsestudent56

Doesn’t multiplying both sides by sin x lose a solution? When I cross multiplied I also got a solution of x=90

cosec(90) = 1.

cot(90) = 0

Original post by mqb2766

cosec(90) = 1.

cot(90) = 0

cot(90) = 0

ahh ok. So when answering a question like this, can i just cancel out the sin x from both sides? or should I find the solutions first and then plug it in to see if it makes sense in the original equation? I've been told to never cancel out trig because I might lose a solution

Original post by Gcsestudent56

ahh ok. So when answering a question like this, can i just cancel out the sin x from both sides? or should I find the solutions first and then plug it in to see if it makes sense in the original equation? I've been told to never cancel out trig because I might lose a solution

Fair enough, I was just trying to illustrate that validating a "solution" is usually a good idea. The key thing is to factorise so

cosec(x) - 2cos(x)/sin(x) = cosec(x) - 2cos(x)cosec(x) = cosec(x)(1 - 2cos(x)) = 0

on the domain 0<x<180, cosec(x) > 0 so there are no solutions associated with it.

Yeah, you do lose a solution. Preferable to do it the other way i.e cross multiplying and then subtracting sin x from both sides or directly subtracting from cosec x. If you cross multiply, you get two answers: x=60 and x=0 or 180 (not 90 tho. sin (90) = 1). However, the questions asks us not to incluse 0 or 180 so you only write 60 as the answer.

Original post by WordsFiddle

Yeah, you do lose a solution. Preferable to do it the other way i.e cross multiplying and then subtracting sin x from both sides or directly subtracting from cosec x. If you cross multiply, you get two answers: x=60 and x=0 or 180 (not 90 tho. sin (90) = 1). However, the questions asks us not to incluse 0 or 180 so you only write 60 as the answer.

oh yh mb, don't know where i got 90 from. thanks

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