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Exercise

$\frac{1-cos^2.x}{\csc^2x}$

Step-by-step Solution

1

Expand the fraction $\frac{1-x\cos\left(x\right)^2}{\csc\left(x\right)^2}$ into $2$ simpler fractions with common denominator $\csc\left(x\right)^2$

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

The reciprocal sine function is cosecant: $\frac{1}{\csc(x)}=\sin(x)$

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

Final answer to the exercise

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

Try other ways to solve this exercise

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  • Find the integral
  • Find the derivative
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  • Find the roots
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