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-cos2x/(sinx-cosx)^2

Mathematics
Tutor: None Selected Time limit: 1 Day

I need assistance in what identities I am able to utilize in order to resolve or simplify the double angle identity. I have tried converting the cos2x in all its three forms in order to simplify, however, nothing seems to function.

Apr 14th, 2015

Use the cosine of double argument formula cos 2x = cos2x – sin2x and factor it by using the difference of squares formula cos 2x = cos2x – sin2x = (cos x – sinx)(cos x + sinx).

Then – cos2x / (sin x – cos x)2 = (sin x – cosx)(sin x + cosx) / (sin x – cos x)2 =

(sin x + cosx) / (sin x – cos x).  

If necessary, continue by dividing both the numerator and denominator by cos x

(tan x + 1) / (tan x - 1) =                          note that  tan(π/4) = 1

- (tan x +  tan(π/4)) / (1 - tan x * tan(π/4) ) =                               use the tangent of the sum formula

- tan(x + π/4) 

Apr 14th, 2015

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