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Exercise

$\left(csc\:x\right)^4+\left(cot\:x\right)^4$

Step-by-step Solution

1

Apply the trigonometric identity: $\csc\left(\theta \right)^n$$=\left(1+\cot\left(\theta \right)^2\right)^{\frac{n}{2}}$, where $n=4$

$\left(1+\cot\left(x\right)^2\right)^{2}+\cot\left(x\right)^4$

Final answer to the exercise

$\left(1+\cot\left(x\right)^2\right)^{2}+\cot\left(x\right)^4$

Try other ways to solve this exercise

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  • Find the derivative
  • Integrate using basic integrals
  • Verify if true (using algebra)
  • Verify if true (using arithmetic)
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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Similar Questions Solved

$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2$

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$\tan\left(x\right)\csc\left(x\right)$

$\frac{2+\tan^2\left(x\right)}{\sec^2\left(x\right)}-1$

$csc^2x-1$

Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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