Verify the identity sin ²1-cos²1 1- cot²t = sin ²₁ 1- To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. sin ²t-cos²t 1- cot²t sin ²t-cos²t ( Apply a reciprocal identity. Apply the appropriate even - odd identity. Apply a Pythagorean identity. Apply a quotient identity. 4
Verify the identity sin ²1-cos²1 1- cot²t = sin ²₁ 1- To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. sin ²t-cos²t 1- cot²t sin ²t-cos²t ( Apply a reciprocal identity. Apply the appropriate even - odd identity. Apply a Pythagorean identity. Apply a quotient identity. 4
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 4E
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Question
![**Verifying Trigonometric Identities**
**Objective:**
To verify the given trigonometric identity by transforming one side to match the other side using appropriate trigonometric identities.
### Identity to Verify:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} = \sin^2 t \]
---
### Steps to Verify the Identity:
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
1. Begin with:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} \]
2. Apply the transformations from the dropdown menu:
- **Dropdown Menu Options:**
- Apply a reciprocal identity
- Apply the appropriate even-odd identity
- Apply a Pythagorean identity
- Apply a quotient identity
3. Choose the transformation:
- Apply a Pythagorean identity
### Result:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} = \sin^2 t \]
By correctly applying the trigonometric identities, we can arrive at the desired result, verifying the given trigonometric identity.
---
For more examples and a step-by-step guide, view an example or get more help using the support options available.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff184a1-2c1e-42c2-8527-d6b5d9856587%2Fa3992e33-a638-4988-a80d-7dc7dffaa852%2Frdg9idn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Verifying Trigonometric Identities**
**Objective:**
To verify the given trigonometric identity by transforming one side to match the other side using appropriate trigonometric identities.
### Identity to Verify:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} = \sin^2 t \]
---
### Steps to Verify the Identity:
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
1. Begin with:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} \]
2. Apply the transformations from the dropdown menu:
- **Dropdown Menu Options:**
- Apply a reciprocal identity
- Apply the appropriate even-odd identity
- Apply a Pythagorean identity
- Apply a quotient identity
3. Choose the transformation:
- Apply a Pythagorean identity
### Result:
\[ \frac{\sin^2 t - \cos^2 t}{1 - \cot^2 t} = \sin^2 t \]
By correctly applying the trigonometric identities, we can arrive at the desired result, verifying the given trigonometric identity.
---
For more examples and a step-by-step guide, view an example or get more help using the support options available.
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