Hey guys, I'm having a little problem with this:
sin^2xcosx = (cos^2x - 2cos^4x + cos^6x)(sinx)
How do I solve this, from one side only? Nothing that I try gets me anywhere! Thanks for your help!
sin^2xcosx = (cos^2x - 2cos^4x + cos^6x)(sinx)
How do I solve this, from one side only? Nothing that I try gets me anywhere! Thanks for your help!
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I don't think you can
But you'd start with the rhs
(cos^2(x) - 2cos^4(x) + cos^6(x))/sin(x)
= cos^2(x) (1 - 2cos^2(x) + cos^4(x))/sin(x)
= cos^2(x)( 1 - cos^2(x))^2/sin(x)
= cos^2(x) (sin^2(x))^2/sin(x)
= cos^2(x)sin^3(x)
= cos(x)sin(x)sin^2(x)cos(x)
So, maybe it's an equation, rather than an identity.....
But you'd start with the rhs
(cos^2(x) - 2cos^4(x) + cos^6(x))/sin(x)
= cos^2(x) (1 - 2cos^2(x) + cos^4(x))/sin(x)
= cos^2(x)( 1 - cos^2(x))^2/sin(x)
= cos^2(x) (sin^2(x))^2/sin(x)
= cos^2(x)sin^3(x)
= cos(x)sin(x)sin^2(x)cos(x)
So, maybe it's an equation, rather than an identity.....