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

Exercise

sin⁡(2x)+sin⁡(x)−2cos⁡2(x)−cos⁡(x)\frac{\sin\left(2x\right)+\sin\left(x\right)}{-2\cos^2\left(x\right)-\cos\left(x\right)}

Step-by-step Solution

1

Factor the polynomial −2cos⁡(x)2−cos⁡(x)-2\cos\left(x\right)^2-\cos\left(x\right) by it's greatest common factor (GCF): −cos⁡(x)-\cos\left(x\right)

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

Final answer to the exercise

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

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