Q. 465.0( 2 Votes )

If <span lang="EN

Answer :

Given,


P(x) = …(1)


P(y) =


P(x).P(y) =


P(x).P(y) =


We know that-


cos x cos y + sin x sin y = cos (x – y)


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


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


P(x).P(y) =


In comparison with equation 1 we can say that:


…(2)


P(x).P(y) = P(x + y)


Similarly, we can show for P(y).P(x):


P(y).P(x) =


By matrix multiplication, we have –


P(y).P(x) =


P(y).P(x) =


P(y).P(x) = …(3)


From equation 2 and 3:


P(x).P(y) = P(y).P(x) = P(x + y) …ans


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