Question

Prove that cos 2x cos x/2 - cos 3x cos 9x/2 = sin 5x sin 5x/2

Answer 1

hii ✌️

here is ur answer...

cos2xcos(x/2)-cos3xcos(9x/2)

=(1/2)[2cos2xcos(x/2)-2cos3xcos(9x/2)]

=(1/2)[cos(2x+x/2)+cos(2x-x/2)-cos(3x+9x/2)-cos(3x-9x/2)]
[∵, 2cosAcosB=cos(A+B)+cos(A-B)]

=(1/2)[cos(5x/2)+cos(3x/2)-cos(15x/2)-cos(-3x/2)]

=(1/2)[cos(5x/2)+cos(3x/2)-cos(15x/2)-cos(3x/2)] [∵, cos(-A)=cosA]

=(1/2)[cos(5x/2)-cos(15x/2)]

=(1/2)[2sin{(5x/2+15x/2)/2}sin{(15x/2-5x/2)/2}] 
[∵, cosC-cosD=2sin(C+D)/2sin(D-C)/2]

=(1/2)×2[sin{(20x/2)/2}sin{(10x/2)/2}]

=sin(10x/2)sin(5x/2)

=sin5xsin(5x/2)

(proved)

hope it will help you

Answer 2

Answer:

thx

Step-by-step explanation: