已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?

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已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?f(co

已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?
已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?

已知f(cosx/2)=3cosx+2,则f(sinπ/8)=?
f(cosx/2)=3cosx+2=6cos^2(x/2)-1
f(x)=6x^2-1
f(sinπ/8)=6sin^2(π/8)-1=6sin^2(π/8)-3+2
=2-3(1-2sin^2(π/8))
=2-3cosπ/4
=2-3√2/2