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Chapter 5: Problem 53

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\frac{\cos ^{2} y}{1-\sin y}$$

Short Answer

Expert verified
The simplified form of the given expression is \(1 + \sin y\)

Step by step solution

01

Recognize and Apply Trigonometric Identity

Apply the Pythagorean identity 锟� for sine and cosine functions. Rewrite \(\cos^2 y\) as \(1 - \sin^2 y\). This transforms our original equation, \(\frac{\cos^2 y}{1-\sin y}\), into \(\frac{1 - \sin^2 y}{1-\sin y}\)
02

Factor and Simplify

We now can factor out the equation \(\frac{1 - \sin^2 y}{1-\sin y}\) into \(\frac{(1 - \sin y)(1+\sin y)}{1-\sin y}\). Simplifying the equation then gives \(1 + \sin y\)
03

Final Solution

The final simplified expression for the given problem is \(1 + \sin y\).

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Most popular questions from this chapter

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\frac{\cos x \cot x}{1-\sin x}=3$$

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Find the \(x\) -intercepts of the graph. $$y=\sin \frac{\pi x}{2}+1$$
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