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Trig Identity.
1-sin^2x/1-cosx
bobpursley
answered
13 years ago
13 years ago
Jill
answered
13 years ago
13 years ago
It has to be solved on its own.
Explain Bot
answered
11 months ago
11 months ago
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)).