MT【62】柯西求三角值域
求$sinx(\sqrt{cos^2x+24}-cosx)$的范围.
解答:[-5,5]
$$\because (sinx \sqrt{cos^2x+24}-cosxsinx)^2$$
$$\le (sin^2x+cos^2x)(cos^2x+24+sin^2x)=25$$
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求$sinx(\sqrt{cos^2x+24}-cosx)$的范围.
解答:[-5,5]
$$\because (sinx \sqrt{cos^2x+24}-cosxsinx)^2$$
$$\le (sin^2x+cos^2x)(cos^2x+24+sin^2x)=25$$
