- #1
jigoku_snow
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Homework Statement
1) how to prove that sin square x cos square x is identical to 1/8 (1-
cos 4x)?
2) f(x) = x square +7x -6
----------------, show that when x is sufficiently small for
(x-1)(x-2)(x+1)
x^4 and higher powers to be neglected.
Homework Equations
1) cos (s + t) = cos s cos t – sin s sin t
cos 2t = cos2 t – sin2 t = 2 cos2 t – 1 = 1 – 2 sin2 t
sin 2t = 2 sin t cos t
2) A Bx + C
--------- + ------------
factor quadractic
The Attempt at a Solution
1) from RHS:
1- cos (2x +2x) 1-[ cos 2x cos 2x - sin 2x sin 2x]
-------------- = ----------------------------------
8 8
1- cos^4 x + sin^4 x + 6 sin^2 x cos^2 x
----------------------------------------
8
* how to do the next step? is my solutions are correct so far?
2) (x^2+7x-6)(x-1)^-1 ( x-2)^-1 (x+1)^-1
expand (x-1)^-1 = 1+x+x^2+x^3
(x-2)^-1 = 1/2 + x/4 + x^2/8 + x^3/16
(1+x)^-1 = 1- x + x^2 - x^3
multiply all : (x^2+7x-6)(1+x+x^2+x^3)( 1/2 + x/4 + x^2/8 + x^3/16)
(1- x + x^2 - x^3)
= 3x^2/2 - x^3/4 +2x -3
* however , the answer I obtain is wrong. which part of my solution is
wrong?