Prove that cos4(θ)−sin4(θ)=cos⁡(2θ) So, here are my steps so far: (cos2θ)2−(sin2θ)2=cos⁡(2θ) (cos2θ+sin2θ)(cos2θ−sin2θ)=cos⁡(2θ) (cos2θ+sin2θ)(cos⁡θ+sin⁡θ)(cos⁡θ−sin⁡θ)=cos⁡(2θ)

Courtney Griffin

Courtney Griffin

Answered

2022-01-26

Prove that cos4(θ)sin4(θ)=cos(2θ)
So, here are my steps so far:
(cos2θ)2(sin2θ)2=cos(2θ)
(cos2θ+sin2θ)(cos2θsin2θ)=cos(2θ)
(cos2θ+sin2θ)(cosθ+sinθ)(cosθsinθ)=cos(2θ)

Answer & Explanation

nebajcioz

nebajcioz

Expert

2022-01-27Added 15 answers

Well, cos2(θ)+sin2(θ)=1, and cos(2θ)=cos2(θ)sin2(θ) is a standard Double-Angle identity.
Prince Huang

Prince Huang

Expert

2022-01-28Added 15 answers

We have
cos4(θ)sin4(θ)=(cos2θ+sin2θ)(cos2θsin2θ)
where (cos2θ+sin2θ)=1 and (cos2θsin2θ)=2cos2(θ)1=cos(2θ)

2022-01-31

No the answer is /cos sintheta 7

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