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f(x)=cos(4x)sin(2x)+cos(7x)sin(x)cos(13x)sin(5x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

cos4xsen2x+cos7x.senx+cos13xsen5xcos4xsen2x+cos7x.senx+cos13xsen5x

Step-by-step Solution

Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression cos(4x)sin(2x)+cos(7x)sin(x)cos(13x)sin(5x). Apply the trigonometric identity: \sin\left(x\right)\cos\left(y\right)=\frac{\sin\left(x+y\right)+\sin\left(x-y\right)}{2}. Combine fractions with common denominator 2. Combine fractions with common denominator 2. Use the odd-even identity \sin(-\theta)=-\sin(\theta).
Simplify the trigonometric expression cos(4x)sin(2x)+cos(7x)sin(x)cos(13x)sin(5x)

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Final answer to the exercise

−sin⁡(2x)+sin⁡(18x)2\frac{-\sin\left(2x\right)+\sin\left(18x\right)}{2}

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

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

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

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

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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cos4xsen2x+cos7x.senx+cos13xsen5x
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