Simplify cos^4(x)-sin^4(x)=sqrt(3)sin(2x) and solve on the interval [0,pi)

[goat]

I know this has to do with double angle identities but I have no clue where to start on this.
Simplify cos^4(x)-sin^4(x)=sqrt(3)sin(2x) and solve on the interval [0,pi)

thanks for any help you can give me

 

[goat]

I know this equation uses double angle identities but I don't know where to start on it. Do I expand the sin(2x) or bring it over to the other side of the equation? I know how to solve for x with k values but I don't know how to get up to that point.
cos^4(x)-sin^4(x)=sqrt(3)sin(2x)
Thanks for any help you are able to give.

 

[Deleted member 4993]

I know this equation uses double angle identities but I don't know where to start on it. Do I expand the sin(2x) or bring it over to the other side of the equation? I know how to solve for x with k values but I don't know how to get up to that point.
cos^4(x)-sin^4(x)=sqrt(3)sin(2x)
Thanks for any help you are able to give.

Factorize

cos⁴(x) - sin⁴(x)

and simplify...

 

[Bob Brown MSEE]

remember

Factorize

cos⁴(x) - sin⁴(x)

and simplify...

x² - y² = (x-y)(x-y)

so let
x = cos²(x)
and
y = sin²(x)

(Following Subhotosh Khan's advice)