1. f(x)=sinx+13sin3x+25sin5x f′(x)=cosx+cos3x+2cos5xf′(x)=0⇔2cos3xcos2x+2cos4xcosx=0⇔(4cos3x−3cosx)cos2x+cos4x.cosx=0⇔cosx((2cos2x−1)cos2x+2cos22x−1)=0 Đáp số: [x=π2+kπ(k∈Z)x=±α2+kπ(k∈Z,cosα=1+√178)x=±β2+kπ(k∈Z;cosβ=1√178) 2. Dễ chứng minh tanA2tanB2+tanB2tanC2+tanC2tanA2=1 nên đpcm ⇔cosC2(sinA2cosB2+sinB2cosA2)+sinC2(cosA2cosB2−sinA2sinB2)=1 ⇔cosC2.sinA+B2+sinC2.cosA+B2=1 ⇔cos2C2+sin2C2=1 (đúng)
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