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Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
Proving Trigonometric Identities
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Proving Trigonometric Identities

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

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

Published in: Education, Technology
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Notes
  • Again, thanks all for leaving such nice comments, I'm so glad you found this useful... I made a quick video on the problem @jeserycabansag posted, it's handwritten and it's been a while since I've done one of these but I hope it will still be helpful... http://www.educreations.com/lesson/view/another-trig-equation-solved/9464621/?s=mUeOfh&ref=appemail
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  • @jeserycabansag sec + tan is the same as saying 1/cos + sin/cos
    find the common denominator which will be cos . treat it like a fraction . so 1+sin over the common denominator which is cos. since cos into cos times 1 = 1 . and cos into cos times sin = sin. therefore your answer will be 1+sin/cos
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  • @jeserycabansag
    separate them out like 1/cosx +sinx/cosx
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  • pls prove 1-(cos^2/1+sin)=sin
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  • pls prove 1+sin/cos=sec+tan
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  • 1. TRIGONOMETRY Proving Trigonometric Identities
  • 2. REVIEW Quotient Identities Reciprocal Identities Pythagorean Identities
  • 3. Let’s start by working on the left side of the equation….
  • 4. Rewrite the terms inside the second parenthesis by using the quotient identities
  • 5. Simplify
  • 6. To add the fractions inside the parenthesis, you must multiply by one to get common denominators
  • 7. Now that you have the common denominators, add the numerators
  • 8. Simplify
  • 9. Since the left side of the equation is the same as the right side, you’ve successfully proven the identity!
  • 10. On to the next problem….
  • 11. Let’s start by working on the left side of the equation….
  • 12. We’ll factor the terms using the difference of two perfect squares technique
  • 13. Using the Pythagorean Identities the second set of parenthesis can be simplified
  • 14. Since the left side of the equation is the same as the right side, you’ve successfully proven the identity!
  • 15. On to the next problem….
  • 16. Let’s start by working on the right side of the equation….
  • 17. Multiply by 1 in the form of the conjugate of the denominator
  • 18. Now, let’s distribute in the numerator….
  • 19. … and simplify the denominator
  • 20. ‘ Split’ the fraction and simplify
  • 21. Use the Quotient and Reciprocal Identities to rewrite the fractions
  • 22. And then by using the commutative property of addition…
  • 23. … you’ve successfully proven the identity!
  • 24. One more….
  • 25. Let’s work on the left side of the equation…
  • 26. Multiply each fraction by one to get the LCD
  • 27. Now that the fractions have a common denominator, you can add the numerators
  • 28. Simplify the numerator
  • 29. Use the Pythagorean Identity to rewrite the denominator
  • 30. Multiply the fraction by the constant
  • 31. Use the Reciprocal Identity to rewrite the fraction to equal the expression on the right side of the equation

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