Jackson L.

asked • 01/11/16

show that(sinx - cosx)/(sinx+cosx) = (2sin^2x-1)/(1 + 2sinxcosx)

pre calculus

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Brian O. answered • 01/11/16

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LHS
(sin x - cos x)/(sin x + cos x)
= (sin2x - cos2x)/(sin x + cos x)2
= (2sin2x -1)/(sin2x+cos2x +2 sin x cos x)
= (2 sin2x -1)/(1 + 2 sin x cos x)
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Jackson L.

How do you go from sinx -cosx to sin^2x -cos^2x
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01/11/16

Brian O.

Multiplying the numerator and denominator of the original trig fraction by (sin x + cos x)
The numerator becomes (sin x - cos x)(sin x + cos x) = sin2x - cos2x (difference of two squares)
The denominator = (sin x + cos x)2
 
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01/11/16

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