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19 March, 04:55

Prove csc^4x-2csc^2x+1=cot^4x

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  1. 19 March, 06:59
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    csc^4 x - 2 csc² x + 1 =

    = 1 / sin^4 x - 2 / sin² x + 1 =

    = (1 - 2 sin² x + sin^4 x) / sin^4 x =

    = (sin² x - 1) ² / sin^4 x =

    = (cos² x) ² / sin^4 x = cos^4 x / sin^ 4 x = cot ^4 x
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