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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.

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• 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