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f(x)=(sin(2x)+cos(2x)+-1)/(sin(2x)+cos(2x)+1)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

sin⁡(2x)+cos⁡(2x)−1sin⁡(2x)+cos⁡(2x)+1\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⁡(x+π4)=sin⁡(x)2+cos⁡(x)2\sin\left(x+\frac{\pi}{4}\right)=\frac{\sin\left(x\right)}{\sqrt{2}}+\frac{\cos\left(x\right)}{\sqrt{2}}

sin⁡(2x)+cos⁡(2x)−12sin⁡(2x+45)+1\frac{\sin\left(2x\right)+\cos\left(2x\right)-1}{\sqrt{2}\sin\left(2x+45\right)+1}

Final answer to the exercise

sin⁡(2x)+cos⁡(2x)−12sin⁡(2x+45)+1\frac{\sin\left(2x\right)+\cos\left(2x\right)-1}{\sqrt{2}\sin\left(2x+45\right)+1}

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