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virtus

  • 3 years ago

Show that cos(4)x =8(cos^(4)x -cos^(2)x)+1

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  1. ganeshie8
    • 3 years ago
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    start by factoring out cos^2 from first two terms

  2. virtus
    • 3 years ago
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    8cos^2(cos^2x -cosx)+1

  3. ganeshie8
    • 3 years ago
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    \(\huge 8(cos^4x -cos^2x) + 1\) is this the RHS ?

  4. virtus
    • 3 years ago
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    yes

  5. y2o2
    • 3 years ago
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    \[\large L.H.S = [ 8\cos^ 2(x)(\cos^2(x) - 1) ]+1 = [ -8\cos^ 2(x)\sin^2(x) ]+1 \] \[\large = [ -2 (2\sin(x)\cos(x))^2 ]+1 = [-2(\sin(2x) ) ^2 ] + 1 \] \[\large = 1-2\sin^2(2x) = \cos^2(2x) - \sin^2(2x) = \cos(4x) = R.H.S\]

  6. ganeshie8
    • 3 years ago
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    good work @y2o2 :)

  7. virtus
    • 3 years ago
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    thanks guys, i will look at this later because i am super sleepy

  8. y2o2
    • 3 years ago
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    @ganeshie8 Thank you :)

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