sinxcos y = 1/2(sin(x + y) + cos(x – y)) TRUE OR FALSE

Question

sinxcos y = 1/2(sin(x + y) + cos(x – y)) TRUE OR FALSE

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Katherine 2 weeks 2021-09-10T10:19:57+00:00 1 Answer 0

Answers ( )

  1. Answer:

    False

    sin x cos y \neq\frac{\bf 1}{\bf 2} (sin (x + y) + cos (x – y))

    Step-by-step explanation:

    Given \sin x \cos y = 1/2(\sin(x + y) + \cos(x - y))\hfill (1)

    To verify  that the equality is true or false

    \sin (x+y)=\sin x \cos y+ \cos x \sin y  and

    \cos (x-y)=\cos x \cos y+ \sin x \sin y

    Now adding the above equations we get

    \sin (x+y)+ \cos (x-y)= \sin x \cos y+ \cos x \sin y+ \cos x \cos y+ \sin x \sin y\hfill (2)

    Comparing  the equations (1) and (2) we get

    \sin x \cos y \neq \frac {1}{2} \(sin (x + y) + \cos (x - y))

    Therefore the given equality is not true (ie, false)

             

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