Anonymous
Anonymous asked in 科學及數學數學 · 1 decade ago

Maths ( prove identities )

I want to ask if someone is able to prove these identities questions, thank

you. ^ means over

sin^(6) x + cos ^(6) x identities 1- 3 sin^ (2)x [cos^(2) x ]

{sin^(2) x [cos ^(4) x] + sin^(4) x [cos ^( 2 ) x } tan^(2) x identities sin^(4) x

I am urgent to know the answer, thank you.

1 Answer

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    Lv 7
    1 decade ago
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    1. sin^6 (x) + cos^6 (x) identities 1-3 sin^2 (x)cos^2 (x)

    Sol

    sin^6 (x)+cos^6 (x)

    (sin^2 (x)+cos^2 (x))(sin^4 (x)-sin^2 (x) cos^2 (x)+cos^4 (x))

    =(sin^4 (x)-sin^2 (x)cos^2 (x)+cos^4 (x))

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

    =(sin^2 (x)+cos^2 (x))^2-3sin^2 (x) cos^2 (x)

    =1-3sin^2 (x) cos^2 (x)

    {sin^2 (x) [cos ^4 (x)] + sin^4 (x) [cos ^ 2 (x)]} tan^2 (x) identities sin^4 (x)

    {sin^2 (x) [cos ^4 (x)] + sin^4 (x) [cos ^ 2 (x)]} tan^2 (x)

    =sin^2 (x)cos ^2 (x) { cos ^2 (x) + sin^2 (x)} tan^2 (x)

    =sin^2 (x)cos ^2 (x) tan^2 (x)

    =sin^2 (x)cos ^2 (x)[sin^2 (x)/cos ^2 (x)]

    = sin^4 (x)

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