If (F/(sin (A − a))) = (W/(sin A)), prove that tan A = ((W sin a)/(W cos a − F))


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Question Number 20648 by Joel577 last updated on 30/Aug/17

$If \frac{F}{\sin (A - a)} = \frac{W}{\sin A}, prove that$ $\tan A = \frac{W \sin a}{W \cos a - F}$
	Answered by $@ty@m last updated on 30/Aug/17

	$G i v e n,$ $\frac{F}{\sin (A - a)} = \frac{W}{\sin A}$ $\Rightarrow F s i n A = W s i n (A - a)$ $\Rightarrow F s i n A = W s i n A c o s a - W c o s A s i n a$ $\Rightarrow F t a n A = W t a n A c o s a - W s i n A$ $(d i v i d i n g t h e e q n . b y c o s A)$ $\Rightarrow W s i n A = t a n A (W c o s a - F)$
	Commented by Joel577 last updated on 31/Aug/17

	$t h a n k y o u v e r y m u c h$
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