Trig Identity.
1-sin^2x/1-cosx
Identity? Where is the equal sign?
It has to be solved on its own.
To simplify the given trigonometric expression, we can use the identity:
1 - sin^2(x) = cos^2(x)
Now, let's substitute this identity into the expression:
(1 - sin^2(x))/(1 - cos(x))
(cos^2(x))/(1 - cos(x))
Next, we can factor out a common term in the denominator:
cos^2(x)/(1 - cos(x))
Now, we can simplify further by using another trigonometric identity:
cos^2(x) = 1 - sin^2(x)
Substituting this identity into the expression:
(1 - sin^2(x))/(1 - cos(x))
(1 - sin^2(x))/(1 - (1 - sin^2(x)))
(1 - sin^2(x))/(1 - 1 + sin^2(x))
(1 - sin^2(x))/(sin^2(x))
Finally, since sin^2(x) / sin^2(x) = 1, we have:
1/(sin^2(x))
Therefore, the simplified form of the given trigonometric expression is 1/(sin^2(x)).