Question #5adf9

2 Answers
Apr 3, 2016

Answer:

Multiply by the conjugate.

Explanation:

#(sinx - cosx) / (sinx + cosx) xx (sinx - cosx)/(sinx - cosx)#

#(sin^2x - 2cosxsinx + cos^2x)/(sin^2x - cos^2x)#

Now, you must apply the pythagorean identity #cos^2x + sin^2x = 1#

#(1 - 2cosxsinx)/(sin^2x + sin^2x - 1)#

#(1 - 2cosxsinx)/(2sin^2x - 1)#

Thus, you have your answer.

Hopefully this helps.

Apr 3, 2016

Answer:

#-cot(pi/4+x)#.

Explanation:

Numerator is #-sqrt2(cos x cos (pi/4)-sinx sin (pi/4))=-cos(pi/4+x)#.
Denominator is #sqrt2(sin x cos (pi/4)+cos x sin (pi/4))=sin(pi/4+x)#.
So, the ratio is #-cot (pi/4+x)#..