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Question

Find an example to show that, in general, each statement is true.

cos (a -b) \neq cos a -cos b

Solution

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Answered 2 years ago
Answered 2 years ago
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1 of 2

Take x=y=90°x=y=90\text{\textdegree}.

Then,

cos(xy)=cos(90°90°)=cos0°=1\cos(x-y)=\cos (90\text{\textdegree}-90\text{\textdegree})=\cos 0\text{\textdegree}=1

cosxcosy=cos90°cos90°=00=0\cos x-\cos y=\cos 90\text{\textdegree}-\cos 90\text{\textdegree}=0-0=0

So, statement cos(xy)cosxcosy\cos (x-y)\ne \cos x-\cos y is true for x=y=90°x=y=90\text{\textdegree}.

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