solve sinxsin3x =1/2

Dear student,

As 

sinxsin3x=1/2

1/2*(2sinxsin3x)=1/2 ; multipying and dividing by 2,

Therefore 2sinxsin3x=1

using formula 2sinAsinB=cos(A-B)-cos(A+B)

here 2sixsin3x=cos2x-cos4x

cos2x-cos4x=1

so cos2x=1+cos4x

cos2x=2cos²2x ; using 1+cos2A=2cos²A

Therefore, 1=2cos2x

so, 1/2=cos2x

so, x=30 as cos60=1/2

All the best!

Please approve my answer if you like it!

sinxsin3x = 1/2

2sinxsin3x = 1

cos-2x - cos4x = 1                        (2sinasinb = cosa-b - cosa+b)

cos2x - cos4x  = 1       ...........1

cos4x = 2cos²2x - 1 so eq 1 becomes

cos2x - (2cos²2x-1) = 1

cos2x - 2cos²2x = 0

cos2x(1-2cos2x) = 0

cos2x = 0                         or                   1-2cos2x = 0

2x = (2n+1)pi/2                                      2x = 2npi +(-)pi/3

x = (2n+1)pi/4                 or                   x = npi +(-)pi/6

these are the required solutions of this equation

approve if u like my ans

Approved