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Ask by Hobbs Davies. in Ecuador
Jan 20,2025

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All real numbers are solutions to the equation.

Solución

Solve the equation by following steps:
  • step0: Solve for :
  • step1: Transform the expression:
  • step2: Rewrite the expression:
  • step3: Move the expression to the left side:
  • step4: Calculate:
  • step5: Factor the expression:
  • step6: Calculate:
  • step7: Separate into possible cases:
  • step8: Solve the equation:
  • step9: Find the union:

    The equation
has the solution:
This means that all real numbers are solutions to the equation.

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Beyond the Answer

A fun fact about trigonometric identities is that they have been used for centuries in various cultures to solve astronomical problems. Ancient Greek astronomers, for instance, relied heavily on these functions to understand planetary movements! They discovered relationships and identities that branched out into modern mathematics, showing us how intertwined math and our understanding of the universe can be.
For a more hands-on approach, when tackling equations like this one, it’s beneficial to work methodically. Start by rewriting everything in terms of sine and cosine if needed. Common mistakes include overlooking double angles or misapplying identities like . Remember, patience and accuracy are key in unwinding these trigonometric puzzles—take your time to check each step!

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