Use power-reducing formulas to rewrite

[AlisonWagner]

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?

 

[tiny-tim]

Welcome to PF!

Hi Alison! Welcome to PF!

(try using the X² button just above the Reply box )

152/4 (1^2 - cos^2 2x), 30(1-(1+cos4x/2)

Nooo

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

 

[LCKurtz]

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?

$\frac{152} 4 = 38$.

 

[AlisonWagner]

and then what would I do after that? Because I know we are supposed to use the power reducing formulas to solve it

 

[AlisonWagner]

Ooh well I guess doing the right math would help me get that...haha thanks for pointing that out! Now I know my mistake!