Алгебра

упростить 1. 19 cos^2 x - 9 + 19 sin^2 x 2. 17 cos^2 x - 5 + 17 sin^2 x 3. (sin^3 x - cos^3 x) / (1 + sinxcosx) +cosx - sinx


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ElizavetaPopova

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1. 19 cos^2 x - 9 + 19 sin^2 x=19(cos^2(x)+sin^2(x))-9=19-9=10 2. 17 cos^2 x - 5 + 17 sin^2 x=17(cos^2(x)+sin^2(x))-5=17-5=12 3. (sin^3 x - cos^3 x) / (1 + sinxcosx) +cosx - sinx= = [(sinx-cosx)(sin^2(x)+sinxcosx+cos^2(x))/(1+sinxcosx)]+cosx-sinx= = [(sinx-cosx)(1+sinxcosx)]/(1+sinxcosx)]+cosx-sinx=sinx-cosx+cosx-sinx=0

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