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Exercise

sin⁡(x)4⋅csc⁡(x)2+cos⁡(x)4⋅sec⁡(x)2\sin\left(x\right)^4\cdot\csc\left(x\right)^2+\cos\left(x\right)^4\cdot\sec\left(x\right)^2

Step-by-step Solution

1

Apply the trigonometric identity: cos⁡(θ)nsec⁡(θ)m\cos\left(\theta \right)^n\sec\left(\theta \right)^m=cos⁡(θ)(n−m)=\cos\left(\theta \right)^{\left(n-m\right)}, where m=2m=2 and n=4n=4

sin⁡(x)4csc⁡(x)2+cos⁡(x)2\sin\left(x\right)^4\csc\left(x\right)^2+\cos\left(x\right)^{2}

Final answer to the exercise

sin⁡(x)4csc⁡(x)2+cos⁡(x)2\sin\left(x\right)^4\csc\left(x\right)^2+\cos\left(x\right)^{2}

Try other ways to solve this exercise

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sin(x)4·csc(x)2+cos(x)4·sec(x)2
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