Find expert answers and community insights on IDNLearn.com. Discover reliable and timely information on any topic from our network of knowledgeable professionals.
Sagot :
To simplify the expression [tex]\(\frac{\sin x}{\sec x + 1}\)[/tex], we need to recall some trigonometric identities and perform the simplification step-by-step. Let's start by analyzing the given expression.
1. Start with the given expression:
[tex]\[ \frac{\sin x}{\sec x + 1} \][/tex]
2. Recall the definition of [tex]\(\sec x\)[/tex]:
[tex]\(\sec x = \frac{1}{\cos x}\)[/tex]
3. Substitute this identity into the expression:
[tex]\[ \frac{\sin x}{\frac{1}{\cos x} + 1} \][/tex]
4. Find a common denominator in the denominator of our fraction:
[tex]\[ \frac{\sin x}{\frac{1 + \cos x}{\cos x}} \][/tex]
5. Simplify the complex fraction by multiplying the numerator and the denominator by [tex]\(\cos x\)[/tex]:
[tex]\[ \frac{\sin x \cdot \cos x}{1 + \cos x} \][/tex]
6. Recognize that this is the simplified form.
Therefore, the simplified expression is:
[tex]\[ \boxed{\frac{\sin x \cos x}{1 + \cos x}} \][/tex]
1. Start with the given expression:
[tex]\[ \frac{\sin x}{\sec x + 1} \][/tex]
2. Recall the definition of [tex]\(\sec x\)[/tex]:
[tex]\(\sec x = \frac{1}{\cos x}\)[/tex]
3. Substitute this identity into the expression:
[tex]\[ \frac{\sin x}{\frac{1}{\cos x} + 1} \][/tex]
4. Find a common denominator in the denominator of our fraction:
[tex]\[ \frac{\sin x}{\frac{1 + \cos x}{\cos x}} \][/tex]
5. Simplify the complex fraction by multiplying the numerator and the denominator by [tex]\(\cos x\)[/tex]:
[tex]\[ \frac{\sin x \cdot \cos x}{1 + \cos x} \][/tex]
6. Recognize that this is the simplified form.
Therefore, the simplified expression is:
[tex]\[ \boxed{\frac{\sin x \cos x}{1 + \cos x}} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.