Find the numeric value of ((2−sin^2 (α))/(cos^2 (α)−tan^2 (α)))


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Question Number 72931 by Maclaurin Stickker last updated on 05/Nov/19

$F i n d t h e n u m e r i c v a l u e o f$ $\frac{2 - \sin^{2} (α)}{\cos^{2} (α) - \tan^{2} (α)}$
	Answered by ajfour last updated on 05/Nov/19

	$s a y α = 0 °$ $n u m e r i c v a l u e = \frac{2}{1} = 2$ $s a y α = 45 °$ $n u m e r i c v a l u e = \frac{2 - \frac{1}{2}}{\frac{1}{2} - 1} = - 3 .$
	Commented by Maclaurin Stickker last updated on 05/Nov/19

	$C a n y o u s o l v e b y f a c t o r i n g$ $t h e e x p r e s s i o n ?$
	Commented by ajfour last updated on 05/Nov/19

	$p e r h a p s s o m e o n e e l s e c a n . .$
	Answered by MJS last updated on 05/Nov/19

	${there}^{'} s no general numeric value .$ $we can express using$ $(1) only \sin α = s$ $\frac{s^{4} - 3 s^{2} + 2}{s^{4} - 3 s^{2} + 1} = \frac{(s - 1) (s + 1) (s^{2} - 2)}{(s^{2} - s - 1) (s^{2} + s - 1)}$ $(2) only \cos α = c$ $\frac{c^{2} (c^{2} + 1)}{c^{4} + c^{2} - 1}$ $(3) only \tan α = t$ $- \frac{t^{2} + 2}{t^{4} + t^{2} - 1}$
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