Us a power reducing formula to simplify 20sin²x. Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.
Us a power reducing formula to simplify 20sin²x. Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.
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°.
Related questions
Question
![**Problem Statement**:
Use a power reducing formula to simplify \(20 \sin^2 x\). Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.
Provide your answer below:
---
**Explanation**:
In this problem, you are tasked with using a power-reducing trigonometric identity to simplify the expression \(20 \sin^2 x\). The goal is to express this in a form where the powers of sine and cosine are no greater than 1.
The power-reducing formula for sine is:
\[
\sin^2 x = \frac{1 - \cos(2x)}{2}
\]
Using this, \(20 \sin^2 x\) can be rewritten as:
\[
20 \left(\frac{1 - \cos(2x)}{2}\right)
\]
Simplifying this expression gives:
\[
10(1 - \cos(2x)) = 10 - 10\cos(2x)
\]
Thus, the equivalent expression for \(20 \sin^2 x\) is \(10 - 10\cos(2x)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24f7b9fc-b934-4e37-ae35-bdc4b8c3050d%2Ffa97f3af-8963-4200-8dba-c7747c6a2579%2Fjdppx14_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**:
Use a power reducing formula to simplify \(20 \sin^2 x\). Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.
Provide your answer below:
---
**Explanation**:
In this problem, you are tasked with using a power-reducing trigonometric identity to simplify the expression \(20 \sin^2 x\). The goal is to express this in a form where the powers of sine and cosine are no greater than 1.
The power-reducing formula for sine is:
\[
\sin^2 x = \frac{1 - \cos(2x)}{2}
\]
Using this, \(20 \sin^2 x\) can be rewritten as:
\[
20 \left(\frac{1 - \cos(2x)}{2}\right)
\]
Simplifying this expression gives:
\[
10(1 - \cos(2x)) = 10 - 10\cos(2x)
\]
Thus, the equivalent expression for \(20 \sin^2 x\) is \(10 - 10\cos(2x)\).
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