Question

Question #5adf9

Answer 1

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.

Answer 2

`-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)`..