Cant seem to find the answer for this question or the correct identity to even begin with so am seeking help... please.
asked Sep 9, 2016 in Trigonometry Answers by anonymous

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1 Answer

cos4x=1-2sin^2(2x)=2-3sin2x,

2sin^2(2x)-3sin2x+1=0=(2sin2x-1)(sin2x-1).

So sin2x=1 or sin2x=1/2. Therefore 2x=π/2, and x=π/4, or 2x=π/6,and x=π/12.

In degrees this is x=45 or 15. Also, since sine is positive in Quadrant 2, 2x=π-π/6=5π/6 and x=5π/12=75 degrees.

CHECK

Substitute each of the 3 values of x into the original equation. We'll use degrees.

x=15: 2x=30; 4x=60; cos4x=1/2=2-3/2 OK

x=45: 2x=90; 4x=180; cos4x=-1=2-3 OK

x=75: 2x=150; 4x=300; cos4x=1/2=2-3/2 OK 

answered Sep 10, 2016 by Rod Top Rated User (429,320 points)
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