How to prove this identity

Question

waheguru · Answer

attachment

anonymous · Answer

idk how

anonymous · Answer

hmm well what is 1/sin^2x?

anonymous · Answer

neverm that don't apply. hm

anonymous · Answer

RH can change to cos^2x

anonymous · Answer

hmm

waheguru · Answer

@lonnie455rich  yea thats what I got but then what to we do

waheguru · Answer

@Yttrium  do you have an idea?

waheguru · Answer

I got as far as

1/(1-cosx) = cos^2x

waheguru · Answer

@amistre64 ?

waheguru · Answer

@hero

anonymous · Answer

ya, im stumped as well. im still thinking though. cant give up yet.

anonymous · Answer

Between the two of you, you already posted the solution.  @waheguru mentioned that 
$$\frac{ 1 }{ 1-\cos ^{2}x } = \cos ^{2} x$$
and @lonnie455rich posted that the right hand side simplifies to 
$$\cos ^{2} x$$
so the left and the right sides are equal!

anonymous · Answer

what is that identity for the LH side that says its = to cos^2x. I cant find it in my trig book

waheguru · Answer

@Matt.Mawson  I dont understand how the LS is equal to the RS

waheguru · Answer

And @Matt.Mawson   we simplified to get it equal to that we didnt find an actual identity

directrix · Answer

@waheguru

The equation you posted is not a trig identity. Perhaps, the instructions are to solve for x.

anonymous · Answer

so you're saying this is unsolvable as an identity. no wonder were stumped lol

anonymous · Answer

That isn't a correct equality. If you simplify the LHS you end up with this:

$$\csc ^{2}x=\cos^{2}x$$
Which isn't true..

directrix · Answer

@lonnie455rich  >>>unsolvable as an identity

Yes, that is what I am saying.

anonymous · Answer

$$\csc^2x \neq \cos^2x$$
is this how you would answer this on a trig test?

phi · Answer

your equation
$$ \frac{1}{1-\cos x} = 1-\sin^2 x $$
is not an identify.
However, you can solve for specific x values that make it true.

anonymous · Answer

if they asked you to prove this equation is that how you would solve it? for the x values.

phi · Answer

@lonnie455rich If they asked to prove it, I would say it is not true in general by providing a counter example. For example, when x= pi/2  cos(pi/2)=0 and sin(pi/2)=1
the equation
$$ \frac{1}{1-\cos x} = 1-\sin^2 x \
\frac{1}{1-0} = 1-1\ \text{ or }
\
1 = 0
$$
is not true.