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Exercise

(cosa+csca)3\left(cosa+csca\right)^3

Step-by-step Solution

1

The cube of a binomial (sum) is equal to the cube of the first term, plus three times the square of the first by the second, plus three times the first by the square of the second, plus the cube of the second term. In other words: (a+b)3=a3+3a2b+3ab2+b3=(cos⁡(a))3+3(cos⁡(a))2(csc⁡(a))+3(cos⁡(a))(csc⁡(a))2+(csc⁡(a))3=(a+b)^3=a^3+3a^2b+3ab^2+b^3 = (\cos\left(a\right))^3+3(\cos\left(a\right))^2(\csc\left(a\right))+3(\cos\left(a\right))(\csc\left(a\right))^2+(\csc\left(a\right))^3 =

cos⁡(a)3+3cos⁡(a)2csc⁡(a)+3cos⁡(a)csc⁡(a)2+csc⁡(a)3\cos\left(a\right)^3+3\cos\left(a\right)^2\csc\left(a\right)+3\cos\left(a\right)\csc\left(a\right)^2+\csc\left(a\right)^3

Final answer to the exercise

cos⁡(a)3+3cos⁡(a)2csc⁡(a)+3cos⁡(a)csc⁡(a)2+csc⁡(a)3\cos\left(a\right)^3+3\cos\left(a\right)^2\csc\left(a\right)+3\cos\left(a\right)\csc\left(a\right)^2+\csc\left(a\right)^3

Try other ways to solve this exercise

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  • Product of Binomials with Common Term
  • FOIL Method
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  • Find the derivative
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  • Integrate by partial fractions
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csc2x−1csc^2x-1

2+tan2xsec2x−1\frac{2+tan^2x}{sec^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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