Question

Answer 1

`@cos^2 x-2sin^2 x=0,25`

`<=>(1-sin^2 x)-2sin^2 x=0,25`

`<=>1-3sin^2 x=0,25`

`<=>sin^2 x=1/4`

`<=>sin x=[+-1]/2`

`<=>[(x=30^o),(x=-30^o):}`

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`@` Đặt `A=sin^6 x+cos^6 x+3sin^2 x cos^2 x`

Ta có:

`A=(sin^2 x+cos^2 x)(sin^4 x -sin^2 x cos^2 x+cos^4 x)+3sin^2 x cos^2 x`

   `=1[(sin^2 x +cos^2 x)^2-3sin^2 x cos^2 x]+3sin^2 x cos^2 x`

   `=1-3sin^2 x cos^2 x+3sin^2 x cos^2 x`

   `=1`

`=>Đpcm`