Hello
I have problem from the A-level revision book, and I have manipulated the problem until I reach this point (everything is correct up to here):
tan(x) = √2 × sin(x) tan (x)
I'm thinking that I can divide both sides by tan(x), which will give me:
1 = √2 × sin(x)
The answer section of the book arrives at the same point, but via a different manipulation of the trig identity: tan(x) = sin(x) / cos(x). But the book seems to divide both sides by cos(x), leaving (like me): √2 = 1 / sin(x). I used the same identity, but I manipulated it differently, originally. I have arrived at the same answer.
My question is: can/should I divide both sides of an equation like this by a trig function of an unknown? Because I know that by dividing both sides of an equation by an unknown will remove a possible answer. For example, in other problems, it could remove the possible answer of x=0. Is that the case here? Am I losing possible answers?
Thanks in advance