Question #0a813

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Answer 1 · 2016-07-29T09:59:07

$LHS=cos3x-sin3x$

$=4cos^3x-3cosx-(3sinx-4sin^3x)$

$=4cos^3x+4sin^3x-3cosx-3sinx$

$=4(cos^3x+sin^3x)-3(cosx+sinx)$

$=4(cosx+sinx)(cos^2x-cosxsinx+sin^2x)-3(cosx+sinx)$

$=4(cosx+sinx)(1-cosxsinx)-3(cosx+sinx)$

$=(cosx+sinx)(4-4cosxsinx-3)$

$=(cosx+sinx)(1-4cosxsinx)=RHS$

Proved