So I rememeber in C2 that we couldn't divide by the trig functions cosx, sinx, tanx as that would lose solutions (because if you divide by cosx, your discarding the possible solution cosx = 0 right?)
It isn't a factor on both sides, so you're not losing it. (It basically becomes part of tan.) If it was cosxsinx=cosxcosx then you wouldn't be able to divide.
It isn't a factor on both sides, so you're not losing it. (It basically becomes part of tan.) If it was cosxsinx=cosxcosx then you wouldn't be able to divide.
So is it only this question where we are allowd to divide by cosine?
Why does this method below give me extra solutions which don't work?
So I rememeber in C2 that we couldn't divide by the trig functions cosx, sinx, tanx as that would lose solutions (because if you divide by cosx, your discarding the possible solution cosx = 0 right?)
So how come here we're allowed to divide by cosx?
If you divide an equation by a variable, you have to be sure that the variable cannot be equal to 0 in the equation (you can't divide by 0), otherwise you'll lose correct solutions.
cos2θ=sin2θ
Think about why cos2θ=0 in this equation. Thus it is safe to divide by cos2θ.
If you divide an equation by a variable, you have to be sure that the variable cannot be equal to 0 in the equation (you can't divide by 0), otherwise you'll lose correct solutions.
cos2θ=sin2θ
Think about why cos2θ=0 in this equation. Thus it is safe to divide by cos2θ.
I see, if cos is 0 sin is not zero so they can't be equal. Is this a special case then or are there other common cases where you know you can divide without losing solutions? How would I be able to see this in an exam?
Also, what I don't understand is how did my method produce extra solutions which were wrong if every step is mathematically correct?
I see, if cos is 0 sin is not zero so they can't be equal. Is this a special case then or are there other common cases where you know you can divide without losing solutions? How would I be able to see this in an exam?
Most of the time you'll be fine if you follow the rule : never divide by a trig function in an equation.
Also, it's useful to think about assumptions when using identities
e.g. tanx=cosxsinx
This is not true when cosx=0. So you have to assume cosx=0 when using this identity.