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Proving Trigonometric Identities

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Some examples of using reciprocal, quotient, and Pythagorean identities to prove trigonometric identities.

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Proving Trigonometric Identities

  1. 1. TRIGONOMETRY Proving Trigonometric Identities
  2. 2. REVIEW Quotient Identities Reciprocal Identities Pythagorean Identities
  3. 3. Let’s start by working on the left side of the equation….
  4. 4. Rewrite the terms inside the second parenthesis by using the quotient identities
  5. 5. Simplify
  6. 6. To add the fractions inside the parenthesis, you must multiply by one to get common denominators
  7. 7. Now that you have the common denominators, add the numerators
  8. 8. Simplify
  9. 9. Since the left side of the equation is the same as the right side, you’ve successfully proven the identity!
  10. 10. On to the next problem….
  11. 11. Let’s start by working on the left side of the equation….
  12. 12. We’ll factor the terms using the difference of two perfect squares technique
  13. 13. Using the Pythagorean Identities the second set of parenthesis can be simplified
  14. 14. Since the left side of the equation is the same as the right side, you’ve successfully proven the identity!
  15. 15. On to the next problem….
  16. 16. Let’s start by working on the right side of the equation….
  17. 17. Multiply by 1 in the form of the conjugate of the denominator
  18. 18. Now, let’s distribute in the numerator….
  19. 19. … and simplify the denominator
  20. 20. ‘ Split’ the fraction and simplify
  21. 21. Use the Quotient and Reciprocal Identities to rewrite the fractions
  22. 22. And then by using the commutative property of addition…
  23. 23. … you’ve successfully proven the identity!
  24. 24. One more….
  25. 25. Let’s work on the left side of the equation…
  26. 26. Multiply each fraction by one to get the LCD
  27. 27. Now that the fractions have a common denominator, you can add the numerators
  28. 28. Simplify the numerator
  29. 29. Use the Pythagorean Identity to rewrite the denominator
  30. 30. Multiply the fraction by the constant
  31. 31. Use the Reciprocal Identity to rewrite the fraction to equal the expression on the right side of the equation

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