# Writing A Trig Expression as an Algebraic Expression

Tags: algebraic, expression, trig, writing
 P: 140 1. The problem statement, all variables and given/known data Write the Trigonometric Expression as an algebraic expression. cos(2arccos 2x) 2. Relevant equations Probably the inverse properties, I'm not sure. 3. The attempt at a solution I know I can rewrite this equation as. u= arccos 2x cos(2cos u=2x) I can also say that the adjacent leg is 2x units long and the hypotenuse is 1 unit long. Then using the pythagorean theorm I can figure the opposite leg to be sqrt(1-4x2) I'm not sure If this is necessary though can someone point me in the right direction? The 2 in front of the arccos is throwing me off because if that wasn't there I would just use the inverse property and cos(arccos 2x) would equal 2x.
 HW Helper P: 6,202 If u=cos-1(2x) then you want to find cos(2u). cos(2u)=cos2u-sin2u=2cos2u-1 = 1-2sin2u and cos2u = (cosu)2
 P: 140 I'm not sure I understand why you'd want to find cos(2u) The answer is supposed to be 8x2-1 and thats the answer listed in the back of the book.
HW Helper
P: 6,202
Writing A Trig Expression as an Algebraic Expression

 Quote by themadhatter1 I'm not sure I understand why you'd want to find cos(2u) The answer is supposed to be 8x2-1 and thats the answer listed in the back of the book.
cos(2cos-1(2x))

if you put u = cos-1(2x), wouldn't cos(2cos-1(2x)) become cos(2u)?
 P: 140 Thanks, now I understand. Once you have simplified it to 2cos2u-1 all you have to do is simplify it with the u in place cos2(arcsin 2x)=2x 2(2x)2-1 8x2-1 Thanks!

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