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anemone
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MHB
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Let $\dfrac{\cos^4 a}{x}+\dfrac{\sin^4 a}{y}=\dfrac{1}{x+y}$ for all real $a,\,b,\,x,\,y$.
Prove that $\dfrac{\cos^8 a}{x^3}+\dfrac{\sin^8 a}{y^3}=\dfrac{1}{(x+y)^3}$
Prove that $\dfrac{\cos^8 a}{x^3}+\dfrac{\sin^8 a}{y^3}=\dfrac{1}{(x+y)^3}$