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Simplify the trigonometric expression $\cos\left(\sqrt{4x}\right)+\sqrt{\cos\left(4x\right)}$

Step-by-step Solution

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Solution

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Step-by-step Solution

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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
  • Integrate by parts
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Final answer to the problem

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Derivative

$\frac{d}{dx}\left(\cos\left(\sqrt{4x}\right)+\sqrt{\cos\left(4x\right)}\right)=\frac{-\sin\left(\sqrt{4x}\right)}{\sqrt{x}}+\frac{-2\sin\left(4x\right)}{\sqrt{\cos\left(4x\right)}}$ See step-by-step solution

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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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