Verified answer

f(x) = 2x^2 -2/3

f(sin x) = 2sin^2(x) - 2/3

2f(cos x) = 4cos^2 (x) - 4/3

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f(sinx)+2f(cosx)= 2sin^2(x) - 2/3 + 4cos^2 (x) - 4/3 = 2- 2cos^2 (x) -2/3 + 4cos^2 (x) -4/3 = 2cos^2 (x)