PreCal (verifying trig identities)
posted by Crystal on .
How would you verify the identity?
sin^1/2xcosxsin^5/2xcosx=cos^3xradsinx

what is rad?

radical

multiply both sides by the sqrt sinx
sinxcosxsinxsin^3x cosx=cos^3x sinx
sinxcosxsinx(1cos^2x)sinxcosx=
sinx(1cosx)sinxcosx+sinxcox^3x=
sinx(1cosxcosx)+sinx cox^3x=
Hmmm. This is telling me the identity does not exist, because sinx(12cosx) is not zero.
check my work. There has to be an error here, but I am certain this is (was ) leading somewhere. 
I read your identity as
(sinx)^(1/2)  cosx  (sinx)^(5/2)*cosx = (cosx)^3 *(sinx)^(1/2)
I picked 30 degrees, and the
left side was NOT equal to the right side.
So the way you typed it, it is not an identity. 
Thanks, Reiny.

I think I have the same book as you Crystal... I have no clue how to solve this thing... :p