Express each of the following as an algebraic sum of sines or cosines :

(i) 2sin 6x cos 4x


(ii) 2cos 5x din 3x


(iii) 2cos 7x cos 3x


(iv) 2sin 8x sin 2x


i) 2sin 6x cos 4x = sin (6x+4x) + sin (6x-4x)


= sin 10x + sin 2x


Using,


2sinAcosB = sin (A+ B) + sin (A - B)


ii) 2cos 5x sin3x = sin (5x + 3x) – sin (5x – 3x)


= sin8x – sin2x


Using,


2cosAsinB = sin(A + B) – sin (A - B)


iii) 2cos7xcos3x = cos (7x+3x) + cos (7x – 3x)


=cos10x + cos 4x


Using,


2cosAcosB = cos (A+ B) + cos (A - B)


iv)2sin8xsin2x = cos (8x - 2x) – cos (8x + 2x)


= cos6x – cos10x


Using,


2sinAsinB = cos (A - B) – cos (A+ B)


1