Answer :

(i)cos(n + 2)x.cos(n + 1)x + sin(n + 2)x.sin(n + 1)x

= sin((n + 2)x + (n + 1)x)(using cos(A - B) = cosAcosB + sinAsinB)


= cos(nx + 2x - (nx + x))


= cos(nx + 2x - nx - x)


= cosx


(ii)


(using cos(A + B) = cosAcosB - sinAsinB)



)


= sin(x + y)


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