Solving Sin(2x) = Cos(2x): A Complete Guide to Trigonometric Equations

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SUMMARY

The equation sin(2x) = cos(2x) can be efficiently solved using a substitution method. By substituting u for 2x, the equation simplifies to sin(u) = cos(u), which is easier to manage. Alternatively, dividing both sides by cos(2x) can also lead to a solution. These methods streamline the process and reduce complexity in solving trigonometric equations.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with double angle formulas
  • Basic algebraic manipulation skills
  • Knowledge of substitution methods in equations
NEXT STEPS
  • Study the double angle formulas for sine and cosine
  • Learn about trigonometric substitution techniques
  • Explore solving trigonometric equations using identities
  • Practice problems involving sin(u) = cos(u) for deeper understanding
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric equations, and anyone seeking to enhance their problem-solving skills in mathematics.

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qweqwe said:
solve the equation sin(2x) = cos(2x)

Tried using the double angle formula

Too much work! Make a simple substitution so you can solve the equation sin(u)=cos(u).
 
If you show what you have done we can help you find the mistake.
 
or just divide by cos(2x)
 

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