Use power-reducing formulas to rewrite

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Homework Help Overview

The problem involves using power-reducing formulas to rewrite the expression 152sin²x cos²x. The subject area is trigonometric identities and simplification.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of power-reducing formulas and share attempts at simplifying the expression. There is a focus on the calculations leading to different results, and some participants question the steps taken in the simplification process.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's attempts. Some guidance has been offered regarding potential simplifications, and there is recognition of mistakes in calculations. Multiple interpretations of the problem are being explored.

Contextual Notes

Participants are working under the constraints of homework rules that require the use of specific formulas. There is also a noted discrepancy between the results obtained and the expected answer, prompting further inquiry.

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Homework Statement


Use power-reducing formulas to rewrite 152sin^2 x cos^2 x

Homework Equations


sin^2θ= 1-cos2θ/ 2 and cos^2θ= 1+cos2θ/2


The Attempt at a Solution


152(1-cos2x/2)(1+cos2x/2), 152/4 (1^2 - cos^2 2x), 30(1-(1+cos4x/2), and I got 30-30+30cos4x/2 as the answer but the answer is supposed to be 19-19 cos4x. I have no idea how that can be?
 
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Hi Alison! Welcome to PF! :smile:

(try using the X2 button just above the Reply box :wink:)
AlisonWagner said:
152/4 (1^2 - cos^2 2x), 30(1-(1+cos4x/2)

Nooo :redface:

(but anyway wouldn't it be simpler to start with sin2xcos2x = (sinxcosx)2 ? :wink:)
 
AlisonWagner said:

Homework Statement


Use power-reducing formulas to rewrite 152sin^2 x cos^2 x

Homework Equations


sin^2θ= 1-cos2θ/ 2 and cos^2θ= 1+cos2θ/2


The Attempt at a Solution


152(1-cos2x/2)(1+cos2x/2), 152/4 (1^2 - cos^2 2x), 30(1-(1+cos4x/2), and I got 30-30+30cos4x/2 as the answer but the answer is supposed to be 19-19 cos4x. I have no idea how that can be?

##\frac{152} 4 = 38##.
 


and then what would I do after that? Because I know we are supposed to use the power reducing formulas to solve it
 
Ooh well I guess doing the right math would help me get that...haha thanks for pointing that out! Now I know my mistake!
 

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