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Chapter 5: Problem 49

Rewrite the expression so that it is not in fractional form. There is more than one correct form of each answer. $$\frac{\sin ^{2} y}{1-\cos y}$$

Short Answer

Expert verified
The expression so that it is not in fractional form can be rewritten to \(1+\cos y\).

Step by step solution

01

Substitute with an equivalent identity

Use the Pythagorean identity for sine and cosine, which is \(\sin^2 y = 1 - \cos^2 y\). This will eliminate the \(\sin^2 y\) in the numerator. So, the given expression is equivalent to \(\frac{1-\cos^2 y}{1-\cos y}\).
02

Factorize the numerator

The numerator can be rewritten as \((1-\cos y)(1+\cos y)\) by way of difference of squares, which simplifies the given expression to \(\frac{(1-\cos y)(1+\cos y)}{1-\cos y}\).
03

Simplify the fraction

Now, the terms \(1-\cos y\) in the numerator and the denominator cancel out each other leaving us with \(1+\cos y\) as the simplified non fractional form of the given expression.

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