factorise the expression sin4x−sinx


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Question Number 10788 by okhema last updated on 25/Feb/17

$f a c t o r i s e t h e e x p r e s s i o n s i n 4 x - s i n x$
	Answered by argemiroQR last updated on 26/Feb/17

	$s i n (3 x + x) - s i n x =$ $s i n 3 x c o s x + c o s 3 x s i n x - s i n x =$ $c o s x (3 s i n x - 4 {s i n}^{3} x) + ({c o s}^{3} x - 3 c o s x) s i n x - s i n x =$ $3 s i n x c o s x - 4 {s i n}^{3^{}} x c o s x + {s i n x c o s}^{3} x - 3 s i n x c o s x - s i n x =$ $s i n x (3 c o s x - 4 {s i n}^{2} x c o s x + {c o s}^{3} x - c o s x - 1)$
	Commented by okhema last updated on 27/Feb/17

	$i a m l a s t f r o m t h e t h i r d l i n e, l i k e y o u$ $s k i p s o m e s t e p s$
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