sin x / 1-cosx is equivalent to:
sin x / 1 + cos x Is this right?
To determine if sin x / 1 - cos x is equivalent to sin x / 1 + cos x, we can simplify both expressions.
Let's start with sin x / 1 - cos x:
sin x / 1 - cos x
Next, let's simplify the denominator by multiplying both the numerator and the denominator by (1 + cos x):
(sin x / 1 - cos x) * (1 + cos x) / (1 + cos x)
Now, we can simplify the expression:
sin x * (1 + cos x) / (1 - cos x + cos x - cos^2 x)
Notice that the denominator simplifies to 1 - cos^2 x, which is a trigonometric identity for sin^2 x. Therefore, we have:
sin x * (1 + cos x) / sin^2 x
Since sin^2 x is the same as (sin x)^2, we can cancel out one sin x from the numerator and the denominator:
(1 + cos x) / sin x
So, sin x / 1 - cos x simplifies to (1 + cos x) / sin x.
Now, let's compare this result with sin x / 1 + cos x:
sin x / 1 + cos x
The expressions sin x / 1 - cos x and sin x / 1 + cos x are not the same. Therefore, sin x / 1 - cos x is not equivalent to sin x / 1 + cos x.
The correct expression for sin x / 1 - cos x is (1 + cos x) / sin x.