" (i) "sin2x+cos x=0quad [N

Prove that nC_ (1) sin x * cos (n-1) x + nC_ (2) sin2x * cos (n-2) x + nC_ (3) sin3x * cos (n-3) x + ... + nC_ ( n) sin nx = 2 ^ (n-1) sin nn

cos ^(3) x sin 2x= sum _(x=0) ^(n) a _(r) sin (rx) AA x in R, then

cos ^(3) x sin 2x = sum _(x =0) ^(n) ar sin (rx) AA x in R, then

Prove that Sigma_(K=0)^(n) ""^nC_(k) sin K x cos (n-K)x = 2^(n-1) sin x.

cos3x-sin2x=0

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

Ltquad x rarr0 (1-cos ^ (2) (sin x) -cos (sin ^ (2) x) + cos ^ (2) (sin x) cos (sin ^ (2) x)) / (x ^ ( 6)) =

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + y)