Question

sin2theta + cos4theta =cos2theta +sin4theta
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Answer 1

Answer:

sin2(θ)+cos4(θ)=cos2(θ)+sin4(θ)

sin2⁡(θ)+cos4⁡(θ)=cos2⁡(θ)+sin4⁡(θ)

I only know how to solve using factoring and the basic trig identities, I do not know reduction or anything of the sort, please prove using the basic trigonometric identities and factoring.

After some help I found that you move the identity around, so:

sin2(θ)−cos2(θ)=sin4(θ)−cos4(θ)sin2⁡(θ)−cos2⁡(θ)=sin4⁡(θ)−cos4⁡(θ)

Then,

sin2(θ)−cos2(θ)=(sin2(θ)+cos2(θ))(sin2(θ)−cos2(θ))sin2⁡(θ)−cos2⁡(θ)=(sin2⁡(θ)+cos2⁡(θ))(sin2⁡(θ)−cos2⁡(θ))