Chứng minh sin(a)^6+cos(a)^6=1-3sin(a)^2*cos(a)^2

Question

Chứng minh sin(a)^6+cos(a)^6=1-3sin(a)^2*cos(a)^2

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Lyla 1 tháng 2021-08-31T08:27:11+00:00 2 Answers 5 views 0

Answers ( )

    0
    2021-08-31T08:28:54+00:00

    $VT= sin^6a+cos^6a$

    $= (sin^2a)^3 + (cos^2a)^3$

    $= (sin^2a+cos^2a)(sin^4a-sin^2a.cos^2a+cos^4a)$

    $= sin^4a-sin^2a.cos^2a+cos^4x$

    $= (sin^2a+cos^2a)^2-2sin^2a.cos^2a-sin^2a.cos^2a$

    $= 1-3sin^2a.cos^2a$

    $= VP$ (đpcm)

    0
    2021-08-31T08:29:10+00:00

    Đáp án:

     

    Giải thích các bước giải:

     Ta có: sin$^{6}$a+cos$^{6}$a=(sin$^{2}$a)$^{3}$+(cos$^{2}$a)$^{3}$

    =(sin$^{2}$a+cos$^{2}$a)(sin$^{4}$a-sin$^{2}$a.cos$^{2}$a+cos$^{4}$a)

    =(sin$^{2}$a+cos$^{2}$a)$^{2}$-3sin$^{2}$a.cos$^{2}$a (vì sin$^{2}$a+cos$^{2}$a)

    =1-3sin$^{2}$a.cos$^{2}$a

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