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18 September, 07:36

Rewrite with only sin x and cos x.

sin 2x - cos 2x

A. 2 sinx cosx - 1 + 2 sin^2x

B. 2 sin x cos^2x - 1 + 2 sin^2x

C. 2 sin x cos^2x - sin x + 1 - 2 sin^2x

D. 2 sin x cos^2x - 1 - 2 sin^2x

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Answers (2)
  1. 18 September, 07:39
    0
    A. 2 sinx cosx - 1 + 2 sin^2 x.

    Step-by-step explanation:

    sin2x = 2 sinx cosx

    cos2x = cos^2x - sin^2x

    So sin2x - cos2x = 2 sinx cosx - (cos^2x - sin^2x)

    But cos^2 x = 1 - sin^2 x, so we have:

    2 sinx cosx - (1 - sin^2 x - sin^2x)

    = 2 sinx cosx - 1 + 2 sin^2 x.
  2. 18 September, 07:51
    0
    A. 2·sin (x) ·cos (x) - 1 + 2·sin^2 (x)

    Step-by-step explanation:

    The double angle identities can be use directly:

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

    The difference of these is ...

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