If p = (sin A) / (1 + cos A), then (sin A) / (1 - cos A) is equal to:

Question

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Given p = (sin A) / (1 + cos A).

We need to find the value of (sin A) / (1 - cos A) in terms of p.

Start with the expression:
Q = (sin A) / (1 - cos A)

Multiply numerator and denominator by (1 + cos A) to rationalize the denominator:
Q = (sin A)(1 + cos A) / [(1 - cos A)(1 + cos A)]

Using the identity (a - b)(a + b) = a^2 - b^2:
Q = (sin A)(1 + cos A) / (1 - cos^2 A)

Since 1 - cos^2 A = sin^2 A:
Q = (sin A)(1 + cos A) / (sin^2 A)

Simplify:
Q = (1 + cos A) / sin A

Recall p = (sin A) / (1 + cos A), so:
1 / p = (1 + cos A) / sin A

Therefore, Q = 1 / p.

Hence, (sin A) / (1 - cos A) = 1 / p.

Answer

Answer

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