Question

(square root 2)tan x cos x - tan x=0 solve for x
I get that I will need to square the whole problem but I'm not sure what it will look like after squaring

Answer 1

can you re-write the question? It is not clear what is under the square root.

Answer 2

yes \[\sqrt{2} \tan x \cos x-\tan x=0\]

Answer 3

so would it be \[2 \tan ^{2} x \cos^{2} x-\tan^{2} x=0\] or is that wrong?

Answer 4

Is the original this
\[ \sqrt{2 \tan x \cos x} - \tan x = 0 \]?

Answer 5

no the square root is only over the 2

Answer 6

ok, then you do not square anything.
factor out tan x
what do you get ?

Answer 7

\[\tan x (\sqrt{2} \cos x-1)=0\] then do I set both equal to zero and solve or not yet?

Answer 8

then do I set both equal to zero. yes.
this is the same old idea: if you multiply two terms like A * B =0
to get 0, then the obvious answer is either A is 0 or B is 0 (or both at the same time)
in this case you have
tan x =0 or (sqrt(2) cos(x) -1) =0

Answer 9

thank you so much for your patience!