Prove that 4cos4x−2cos⁡2x−12cos⁡4x is independent of xI don't know how to proceed. cos⁡4x=2cos2(2x)−1

Vilharjevw7

Vilharjevw7

Answered

2022-01-27

Prove that 4cos4x2cos2x12cos4x is independent of x
I don't know how to proceed. cos4x=2cos2(2x)1

Answer & Explanation

rakije2v

rakije2v

Expert

2022-01-28Added 12 answers

Yes, cos4x=2cos2(2x)1 is useful, also cos2x=1+cos2x2
Now
4cos4x2cos2x12cos4x=4(1+cos2x2)22cos2x12(2cos2(2x)1)
then let cos2x=k.
Ydaxq

Ydaxq

Expert

2022-01-29Added 12 answers

4cos4x2cos2x12cos4x=(1+cos2x)22cos2x12(2cos22x1)=32.

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