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Writing A Trig Expression as an Algebraic Expression 
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#1
Jun1810, 05:14 PM

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(14x^{2}) 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. 


#2
Jun1810, 06:05 PM

HW Helper
P: 6,202

If u=cos^{1}(2x) then you want to find cos(2u).
cos(2u)=cos^{2}usin^{2}u=2cos^{2}u1 = 12sin^{2}u and cos^{2}u = (cosu)^{2} 


#3
Jun1810, 06:26 PM

P: 140

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


#4
Jun1810, 06:33 PM

HW Helper
P: 6,202

Writing A Trig Expression as an Algebraic Expression
if you put u = cos^{1}(2x), wouldn't cos(2cos^{1}(2x)) become cos(2u)? 


#5
Jun1810, 06:51 PM

P: 140

Thanks, now I understand.
Once you have simplified it to 2cos^{2}u1 all you have to do is simplify it with the u in place cos^{2}(arcsin 2x)=2x 2(2x)^{2}1 8x^{2}1 Thanks! 


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