Question

1-cos(8x)(cos(5x)cos(3x)-sin(3x)sin(5x))=sin^2(8x)

Answer 1

Only true if

1-cos(8x)[(cos(5x)cos(3x)-sin(3x)sin(5x)]=sin^2(8x)

LS = 1-cos(8x)[(cos(5x)cos(3x)-sin(3x)sin(5x)]
= 1-cos(8x)[(cos(5x + 3x)]
= 1 - cos^2 (8x)
= sin^2 *x)
= RS

Answer 2

type in 2nd last line

= sin^2 *x) should say
sin^2 (8x) of course