6
Question
If F(x)=⎡⎢⎣cos x−sin x0sin xcos x0001⎤⎥⎦, then F(x).F(y)=
If F(x)=⎡⎢⎣cos x−sin x0sin xcos x0001⎤⎥⎦, then F(x).F(y)=
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Solution
The correct option is C F(x+y)
F(x).F(y)=⎡⎢⎣cos x−sin x0sin xcos x0001⎤⎥⎦⎡⎢⎣cos y−sin y0sin ycos y0001⎤⎥⎦⎡⎢⎣cos x.cos y−sin x.sin y−cos x.sin y−sin x.cos y0sin x.cos y+cos x.sin y−sin x.sin y+cos x.cos y0001⎤⎥⎦⎡⎢⎣cos (x+y)−sin(x+y)0sin (x+y)cos (x+y)0001⎤⎥⎦=F(x+y)
F(x+y)
F(x).F(y)=⎡⎢⎣cos x−sin x0sin xcos x0001⎤⎥⎦⎡⎢⎣cos y−sin y0sin ycos y0001⎤⎥⎦⎡⎢⎣cos x.cos y−sin x.sin y−cos x.sin y−sin x.cos y0sin x.cos y+cos x.sin y−sin x.sin y+cos x.cos y0001⎤⎥⎦⎡⎢⎣cos (x+y)−sin(x+y)0sin (x+y)cos (x+y)0001⎤⎥⎦=F(x+y)
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