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Math Help - [SOLVED] Verify that each trigonometric equation is an identity.

  1. #1
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    [SOLVED] Verify that each trigonometric equation is an identity.

    how do i prove (sin^4 x)-(cos^4 x)= (2sin^2x)-1
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  2. #2
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    Quote Originally Posted by somanyquestions View Post
    how do i prove (sin^4 x)-(cos^4 x)= (2sin^2x)-1
    \sin^4 x-\cos^4 x

    (\sin^2 x)^2-(\cos^2 x)^2

    (\sin^2 x)^2-(1-\sin^2 x)^2

    Expand....
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  3. #3
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    Quote Originally Posted by pickslides View Post
    \sin^4 x-\cos^4 x

    (\sin^2 x)^2-(\cos^2 x)^2

    (\sin^2 x)^2-(1-\sin^2 x)^2

    Expand....
    ?? expand?
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  4. #4
    Senior Member Stroodle's Avatar
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    \left [\sin^2 (x)\right ]^2-\left [ 1-\sin^2 (x)\right ]^2

    =\left [sin^2(x)+(1-sin^2(x))\right ]\left [sin^2(x)-(1-sin^2(x))\right]
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  5. #5
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    Quote Originally Posted by Stroodle View Post
    \left [\sin^2 (x)\right ]^2-\left [ 1-\sin^2 (x)\right ]^2

    =\left [sin^2(x)+(1-sin^2(x))\right ]\left [sin^2(x)-(1-sin^2(x))\right]
    i have no idea what that means but this is what i did:

    sin4 x -(1- 2sin^2 x + sin4 x)
    sin4 x - 1+ 2sin^2 x - sin4 x
    sin4 x's cancel out

    -1+2sin^2 x = 2sin^2 x-1
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  6. #6
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    Quote Originally Posted by somanyquestions View Post
    ?? expand?
    (\sin^2 x)^2-(1-\sin^2 x)^2

    (\sin^2 x)^2-(1-\sin^2 x)(1-\sin^2 x)

    (\sin^2 x)^2-(1-2\sin^2 x+(\sin^2 x)^2)

    (\sin^2 x)^2-1+2\sin^2 x-(\sin^2 x)^2

    finish...
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  7. #7
    Senior Member Stroodle's Avatar
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    That works too
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