prove:
cos*2x=csc*2x-2/csc*2x
I think you must be usint * as the power to, as in ^
right side: (csc^2 x - 2)/csc^2 x
(1-2sin^2x) = 1-2(1-cos^2x)=-1+2cos^2x
which is clearly not an identity.
So I am not certain what your problem is.
Your use of * in the last 3 posts will cause confusion
traditionally
* means multiplication
/ means division and
^ means "to the exponent"
so you want to say
cos^2 x=csc^2 x-2/csc^2 x
but that statement is not true for all x's, I just tried any x and it did not work.
Use brackets to establish the proper order of operations.
To prove the given equation cos(2x) = csc(2x) - 2/csc(2x), we will first simplify the right-hand side (RHS) and then show that it is equal to the left-hand side (LHS).
Starting with the RHS:
csc(2x) - 2/csc(2x)
Let's simplify the expression by finding a common denominator:
= csc(2x) - (2/csc(2x)) * (csc(2x) / csc(2x))
= (csc^2(2x) - 2) / csc(2x)
Now let's substitute the reciprocal trigonometric identities for csc:
= (1/sin^2(2x) - 2) / (1/sin(2x))
= (1 - 2sin^2(2x)) / sin(2x)
We can express the left-hand side (LHS) in terms of sin(2x) using the identity cos(2x) = 1 - 2sin^2(2x):
LHS = cos(2x) = 1 - 2sin^2(2x)
Now we can see that LHS = RHS:
LHS = 1 - 2sin^2(2x)
RHS = (1 - 2sin^2(2x)) / sin(2x)
Since both sides are equal, we have proven the equation cos(2x) = csc(2x) - 2/csc(2x).