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Exercise

$\cot^2\left(-2\right)$

Step-by-step Solution

1

Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

$\frac{\cos\left(-2\right)^2}{\sin\left(-2\right)^2}$
Why is cot(x) = cos(x)/sin(x) ?
2

Applying the pythagorean identity: $\cos^2(\theta)=1-\sin(\theta)^2$

$\frac{1- \sin\left(-2\right)^2}{\sin\left(-2\right)^2}$
Why is 1 - sin(x)^2 = cos(x)^2 ?
3

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

$\frac{1}{\sin\left(-2\right)^2}+\frac{- \sin\left(-2\right)^2}{\sin\left(-2\right)^2}$
4

Simplify the resulting fractions

$\frac{1}{\sin\left(-2\right)^2}-1$
5

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\csc\left(-2\right)^2-1$

Final answer to the exercise

$\csc\left(-2\right)^2-1$

Try other ways to solve this exercise

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  • Integrate using basic integrals
  • Verify if true (using algebra)
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  • Product of Binomials with Common Term
  • FOIL Method
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