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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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- 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

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

separate them out like 1/cosx +sinx/cosx