Question

Write the expression in terms of sinx and cosx only: cos^2(2x)-sin(2x)
Please help! This is on the review in our PreCalc textbook (high school junior, please make it so that I can understand, thanks) but there isn't an example in the book that I can understand! Thanks for the help :) By the way, it says the answer should be 1-4sin^2xcos^2x-2sinxcosx.

Answer 1

I don't even know anymore. I don't know what the book wants me to do. I've tried doing it, but I can't get the answer it wants me to... :/ Thanks anyway.

Answer 2

u know sin(2x) = 2 sin(x)cos(x) right?

Answer 3

Sorry I do not know

Answer 4

use the following equations to solve this prob:

sin(2x) = 2sin(x)cos(x) ,
cos(2x) = cos^2(x) - sin^2(x) and
cos^2(2x) = cos(2x)*cos(2x)

it will take a few multiplication n simplification but u will get the right ans. good luck!

Answer 5

y = cos^2 (2x) - sin (2x) = (cos^2 x - sin^2 x)^2 - 2sin x*cos x =
= cos^4 x + sin^4 x - 2(cos^2 x)*(sin^2 x) - 2sin x*cos x. (1).
Find the value of the sum (sin^4 x + cos^4 x)
(sin^4x + cos^4 x) = (sin^2 x + cos^2 x)^2 = 1 =
= sin^4 x + cos^4 x + 2sin^2 x*cos^2 x.
sin^4 x + cos^4 x = 1 - 2sin^2 x*cos^2 x (2)
Substitute this value (2) into equation (1), we get:
y = 1 - 4sin^2 x*cos^2* x - 2sin x*cos x