Simplifying after applying chain rule

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SUMMARY

The discussion focuses on simplifying the expression (Sin2θ)(Cos2θ) using trigonometric identities, specifically the double angle formulas. The final simplified form is established as 1/2(Sin4θ), which is derived from the identity 2sin(x)cos(x) = sin(2x). The participants emphasize the importance of recognizing and applying these identities to achieve the correct simplification in trigonometric problems.

PREREQUISITES
  • Understanding of trigonometric identities, particularly double angle formulas.
  • Familiarity with the sine and cosine functions.
  • Basic knowledge of algebraic manipulation in trigonometric expressions.
  • Experience with calculus concepts, particularly the chain rule.
NEXT STEPS
  • Study the derivation and applications of trigonometric double angle formulas.
  • Learn how to apply the chain rule in calculus problems effectively.
  • Explore advanced trigonometric identities and their proofs.
  • Practice simplifying complex trigonometric expressions using various identities.
USEFUL FOR

Students studying calculus, particularly those focusing on trigonometric functions and identities, as well as educators looking for effective teaching strategies in simplifying trigonometric expressions.

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Homework Statement



http://images.calcchat.com/solutionart/etf5e/03/d/se03d01063.png

Homework Equations





The Attempt at a Solution


I get to the third row, but can't simplify (Sin2θ)(Cos2θ). I'm looking at the trigonometric double angle formulas, and still can't figure out how the final answer came to be 1/2(Sin4θ)
 
Last edited by a moderator:
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2sin(x)cos(x) = sin(2x) .

That should help.
 

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