1) cho sinx+cosx=1/2.tính a) sinx.cosx b) sin^3x+cos^3x c)sin^4x+cos^4x

`\qquad sinx +cos x=1/ 2`

`a)` Ta có:

`\qquad (sinx+cosx)^2=(1/ 2)^2=1/ 4`

`<=>sin^2 x +cos^2x +2sinxcosx=1/ 4`

`<=>1+2sinxcosx=1/ 4`

`<=>2sinxcosx =1/ 4 -1=-3/ 4`

`<=>sinxcosx=-3/ 8`

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`b)` `sin^3x+cos^3x`

`=(sinx+cosx)(sin^2x+cos^2x-sinxcosx)`

`=1/ 2 .[1-(-3/ 8)]`

`=1/ 2 . {11}/8`

`={11}/{16}`

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`c)` `sin^4x+cos^4x`

`=(sin^2x+cos^2x)^2-2sin^2xcos^2x`

`=1^2-2.(sinxcosx)^2`

`=1-2. (-3/ 8)^2`

`=1-9/{32}={23}/{32}`