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Exercise

$\frac{\sin\left(2x\right)+\cos\left(2x\right)-1}{\sin\left(2x\right)+\cos\left(2x\right)+1}$

Step-by-step Solution

1

Apply the addition formula: $\sin\left(x+\frac{\pi}{4}\right)=\frac{\sin\left(x\right)}{\sqrt{2}}+\frac{\cos\left(x\right)}{\sqrt{2}}$

$\frac{\sin\left(2x\right)+\cos\left(2x\right)-1}{\sqrt{2}\sin\left(2x+45\right)+1}$

Final answer to the exercise

$\frac{\sin\left(2x\right)+\cos\left(2x\right)-1}{\sqrt{2}\sin\left(2x+45\right)+1}$

Try other ways to solve this exercise

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