Can someone help me prove the identity of the statement? It has to be step by step with the rule included. ### Proving Trigonometric Identities: An Example#### Example: Verify the identity\[ (1 - \sin^2 x) \csc x = \cos x \cot x \]To prove this identity, we will show each step and the rules applied in transforming the left-hand side (LHS) to make it equal to the right-hand side (RHS).#### Steps:1. **Rewrite the given identity:** \[ (1 - \sin^2 x) \csc x \]2. **Apply the Pythagorean Identity:** Recall that $\sin^2 x + \cos^2 x = 1$, so: \[ 1 - \sin^2 x = \cos^2 x \] Substitute this into our equation: \[ \cos^2 x \csc x \]3. **Rewrite $\csc x$:** Remember that $\csc x = \frac{1}{\sin x}$, so: \[ \cos^2 x \cdot \frac{1}{\sin x} \]4. **Simplify:** Separate the terms: \[ \cos x \cdot \left(\cos x \cdot \frac{1}{\sin x}\right) \] Since $\frac{\cos x}{\sin x} = \cot x$: \[ \cos x \cdot \cot x \]Thus, we have shown that:\[ (1 - \sin^2 x) \csc x = \cos x \cot x \]### Key Points to Remember:- Use the Pythagorean identity: $\sin^2 x + \cos^2 x = 1$- Remember reciprocal identities: $\csc x = \frac{1}{\sin x}$- Simplify step by step, ensuring to apply algebraic transformations correctlyEnsuring each statement is based on a recognized rule or identity helps in systematically proving trigonometric identities. ### Select the RulePlease choose one of the following mathematical rules to explore:- **Algebra**- **Reciprocal**- **Quotient**- **Pythagorean**- **Odd Even** Click on the radio button next to the rule you wish to learn more about. Each rule comes with detailed explanations, examples, and exercises to enhance your understanding.

Answered: Image /qna-images/answer/5a9a5fcc-4e7c-404e-bad8-d93b585777b4.jpg

Answered: Prove the identity. (1- sin'x)c CSCX=…

Math

Trigonometry

Prove the identity. (1- sin'x)c CSCX= COSX cotx

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

See similar textbooks

Related questions

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that if x=4,8,3,-2

Q: Write the converse of the following statement: If it rains today, then I will stay at home.

A: Suppose the statement is "If a then b" then converse of this statement is "If b then a".

Q: 6)- (-1)우. %3D

Q: Write down the dimension of the following set, 4s -3s: s,t in R -t

A: Consider the…

Q: n? O Show that ¬-2n= 0(n²). Show your work and give specific

Q: A AB and intersed otE If m<AEC x-10 ond m< DEB= SX+60 a) Drow a diagrem b)Solve for x ) Find m<CEB

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: snip

Q: A general statement is needed

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Assume that y represents a positive real number. What is the conjugate of Vy - 24?

A: y-24

Q: Find x, and x2- -52 28 -5 5 X2 40 X =

Q: For the AP -3 , -7 ,-11 ... can we find directly a30-a20 without actually finding a30 and a20 ? give…

Q: Evaluate for the given

Q: Let a =(3, -3, 8), and B = (-7, -1, 3), and = (8, 4, 11). Find ||2ä - 36||.

Q: 8) Statements 1. -6(2x +1) = -11x – 7x 1. -12x – 6 = -18x 2. -6 = -6x 3. 4. 1 =x 4. 2. 3.

Q: Find x, and x2- 30 X2 - 46

Q: If x1 = x and x2 = x + Ax, what is Ax?

A: We find ∆x as, x1=xx2=x+∆x⇒x2=x1+∆x⇒x2-x1=x1+∆x-x1⇒x2-x1=∆x⇒∆x=x2-x1

Q: Read the following statement: x + 6 = 6 +x. This statement demonstrates: the substitution property.…

A: Topic = Algebra the reflective property.

Q: State the inverse of the statement, “If there Linah has no ticket then she can leave class.”

Q: Classify the given statement as true or false

A: Statement: Rain is wet or snow is cold. The statement is false.

Q: Evaluate for: x = -2, y = 4, and z = 16 * |-y-x|

A: Given values are x=-2y=4z=16 It is asked to find the value of -y-xz

Q: make the following statement true x=-1 iff, if or only if x2+2x+1

A: Let's find.

Q: The sum of two numbers is 22 and their product is -48. Let x = one of the numbers. Identify all the…

Q: Reasoning. Explain why there is an AA Similarity Postulate but not an AA Congruence Postulate.

A: We have to explain reason behind AA Similarity Postulate but not an AA Congruence Postulate.

Q: Then show the classes that you used for display

A: First make frequency table in proper format: Classes : ( define proper range ) Calculate…

Q: QUESTION 9 Sample 1 Sample 2 5. 12 6. 18 23 4. 17 23 24 6. 6. Using the data set above, what is the…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Decide whether each of the following statements makes sense (or is clearly true) or does not make…

A: Solution: The objective is to decide whether the given statement makes sense or NOT.

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Can someone help me prove the identity of the statement? It has to be step by step with the rule included.

### Proving Trigonometric Identities: An Example

#### Example: Verify the identity

\[ (1 - \sin^2 x) \csc x = \cos x \cot x \]

To prove this identity, we will show each step and the rules applied in transforming the left-hand side (LHS) to make it equal to the right-hand side (RHS).

#### Steps:

1. **Rewrite the given identity:**

\[ (1 - \sin^2 x) \csc x \]

2. **Apply the Pythagorean Identity:**

Recall that $\sin^2 x + \cos^2 x = 1$, so:

\[ 1 - \sin^2 x = \cos^2 x \]

Substitute this into our equation:

\[ \cos^2 x \csc x \]

3. **Rewrite $\csc x$:**

Remember that $\csc x = \frac{1}{\sin x}$, so:

\[ \cos^2 x \cdot \frac{1}{\sin x} \]

4. **Simplify:**

Separate the terms:

\[ \cos x \cdot \left(\cos x \cdot \frac{1}{\sin x}\right) \]

Since $\frac{\cos x}{\sin x} = \cot x$:

\[ \cos x \cdot \cot x \]

Thus, we have shown that:

\[ (1 - \sin^2 x) \csc x = \cos x \cot x \]

### Key Points to Remember:
- Use the Pythagorean identity: $\sin^2 x + \cos^2 x = 1$
- Remember reciprocal identities: $\csc x = \frac{1}{\sin x}$
- Simplify step by step, ensuring to apply algebraic transformations correctly

Ensuring each statement is based on a recognized rule or identity helps in systematically proving trigonometric identities.

### Select the Rule

Please choose one of the following mathematical rules to explore:

- **Algebra**
- **Reciprocal**
- **Quotient**
- **Pythagorean**
- **Odd Even**

Click on the radio button next to the rule you wish to learn more about. Each rule comes with detailed explanations, examples, and exercises to enhance your understanding.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

Kon xp 9+x as t. in xta
What is algebra used for?
Write the following statement as a mathematical statement. Use variable names to denote arbitrary numbers in the domain. Your statements and should be expressed using algebra. "There is no largest integer."
Show that the implication
For each statement below, decide whether that statement is true or false.
Determine x and y such that -2 4 -21 x - Y -4 -4 -1 -6 1 2 4 2x + y x = y =
Give two true statements that involve the symbol 2 and the number 5.
Is the upside T supposed to be a 1? Kind of confusing
if the value of A changes in responce to the value of B, then b is the?