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Exercise

$\sin\left(4x\right)+2\sin\left(2x\right)$

Step-by-step Solution

1

Using the sine double-angle identity: $\sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right)$

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

Factor the polynomial $2\sin\left(2x\right)\cos\left(2x\right)+2\sin\left(2x\right)$ by it's greatest common factor (GCF): $2\sin\left(2x\right)$

$2\sin\left(2x\right)\left(\cos\left(2x\right)+1\right)$

Final answer to the exercise

$2\sin\left(2x\right)\left(\cos\left(2x\right)+1\right)$

Try other ways to solve this exercise

  • Choose an option
  • 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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Similar Questions Solved

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

$1+cot^2x$

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

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

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

$csc^2x-1$

$\frac{2+tan^2x}{sec^2x}-1$

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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