cos^4Θ /cos^2Φ +sin^4Θ/sin^2Φ =1 prove that cos^4Φ/cos^2Θ +sin^4Φ/sin^2Θ =1

Cos^4θ/Cos^ϕ+Sin^4θSin^2ϕ=Cos^2ϕ+Sin^2ϕ
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(Cos^2ϕ−Cos^4θCos^2ϕ)+(Sin^2ϕ−Sin^4θSin^2ϕ)=0
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Cos^4ϕ+Sin^4ϕ=Cos^4θ+Sin^4θ
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SinϕCosϕ = SinθCosθ ⟹ Sin(2ϕ) = Sin(2θ)
So

ϕ=kπ+θ , k∈Z

So

Cosϕ=(−1)^kCosθ, Sinϕ=(−1)^kSinθ