to prove :-

sin3x.sin^3x+cos3x.cos^3x = cos^3*2x

Daer Yash,
Expand Sin3x using formula :

;
sin(2x+x) = cos(2x)sin(x) + sin(2x)cos(x)
Then substitute the double angle formulae for the 2xs
= (cos^2(x) - sin^2(x))sin(x) + 2cos(x)sin(x)cos(x)
// factor out the sinx
= sin(x) (cos^2(x)-sin^2(x) + 2 cos^2(x))
=sin(x) (3cos^2(x) - sin^2(x))

and then reduce the equation to the desired form.

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