Proving-Trigonomddggjhgdsetric-Identities.pptx

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1. PROVING TRIGONOMETRIC IDENTITIES

2. REVIEW Quotient Identities Reciprocal Identities Pythagorean Identities

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….

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….

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….

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