Problem Verifing Identities in Trig

In summary, -The two equations are equal if you replace sin^2(x) on the left side by 1- cos^2(x).-The three most basic formulas for proving trig equations are 1-blank=blank, 1-blank=1, and cot^2x-1/csc^2x =cot^2x/csc^2x-1/csc^2x.
  • #1
Rada3b
4
0
Hello this one has stumped me for about a day and I have tried several different approaches. maybe someone could point me in the right direction.
cot^2x-1/1+cot^2x=2Cos^2x-1

I startedon the Left side tring to prove the equation.

cot^2x-1/csc^2x using Pyth. Theory

(cot^2x/csc^2x)-(1/csc^2x) reciprocal Identites

((cos^2x/sin^2x)/csc^2x)-(sin^2x) reciprocal Identites

(cos^2x/sin^2x)*(sin^2x)-(sin^2x) //sin^2x will cancel outleaving

cos^2x - sin^2x this does not = 2Cos^2x -1

Could somone point me in the right direstion .Thank s in advanced Rada3b
 
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  • #2
Are you sure that

[tex]\cos^2x - \sin^2x = 2\cos^2x - 1[/tex]

is not a true statement? What is 1 equal to in terms of trig identities?
 
  • #3
You are correct it is not. I was trying to prove that the equation on the left is = to the equation on the right in the beginning of the post. Could I simplify the equation on the right anymore that might = cos^2x -sin^2x??
 
  • #4
Yes you can, but taking Tedjins hint =] Ill make it a tiny bit more obvious - Pythagorean identities?
 
  • #5
Tedjn said:
Are you sure that

[tex]\cos^2x - \sin^2x = 2\cos^2x - 1[/tex]

is not a true statement? What is 1 equal to in terms of trig identities?

Rada3b said:
You are correct it is not. I was trying to prove that the equation on the left is = to the equation on the right in the beginning of the post. Could I simplify the equation on the right anymore that might = cos^2x -sin^2x??
"You are correct it is not"? Tedjn was not telling you it is not true! He was suggesting that you check your assumption that it is not true again! Specifically, what do you get if you replace [itex]sin^2(x)[/itex] on the left side by [itex]1- cos^2(x)[/itex]?
 
  • #6
Have you learned about the power reduction formulas yet? It looks easier by using those to me.
 
  • #7
No, we haven't learned the power reduction formula but it sounds a lot easier Hydrargyrum. I will look into it and continue trying. I did sub Pi/4 in for x on both side ofthe equation and yes they are =. So back to proving again, Thanks EV1 for the help.
 
  • #8
Would you PLEASE listen to any of our hints? The power reduction formulas come from what we are trying to tell you. I don't see why our hint, which has become more so an obvious instruction, is so hard to execute?
 
  • #9
Thank you all. I was on the right track.I must be just overstressed atm not to see something so obvious. I got it now.
 
  • #10
Gib Z said:
Would you PLEASE listen to any of our hints? The power reduction formulas come from what we are trying to tell you. I don't see why our hint, which has become more so an obvious instruction, is so hard to execute?

Sorry. I didn't read your posts
 
  • #11
what are the three most basic formulas for proving trig equations?

blank+blank=1
1-blank=blank
1-blank=blank
 
  • #12
L= cot^2x-1/csc^2x =cot^2x/csc^2x -1/csc^2x =(cos^2x/sin^2x)/(1/sin^2x)-sin^2x=cos^2x-sin^2x=cos^2x-(1-cos^2x)=cos^2x-1+ cos^2x=2cos^2x-1=R

Everybody gave you hints. Its been a while now. This should be your answer. Please correct if I am wrong.
 

1. What is the purpose of verifying identities in trigonometry?

The purpose of verifying identities in trigonometry is to prove that two expressions are equivalent to each other. This helps in simplifying complex trigonometric expressions and solving equations involving trigonometric functions.

2. How do I know when to use the Pythagorean identities to verify a trigonometric identity?

The Pythagorean identities, such as sin^2x + cos^2x = 1, are used when the trigonometric expression involves squared terms of sine and cosine. Other trigonometric identities, such as the double angle identities, can be used for different types of expressions.

3. Can I use a calculator to verify trigonometric identities?

Yes, calculators can be used to verify trigonometric identities. However, it is important to understand the steps involved in verifying an identity manually in order to use the calculator effectively.

4. What are some common mistakes to avoid when verifying trigonometric identities?

Some common mistakes to avoid when verifying trigonometric identities include not simplifying both sides of the equation, using the wrong identity, and making calculation errors. It is important to carefully analyze each step and check for any errors before coming to a conclusion.

5. Are there any tips for verifying trigonometric identities more efficiently?

One tip for verifying trigonometric identities more efficiently is to start with the more complex side of the equation and try to simplify it using known identities. Another tip is to work with one side of the equation at a time and make sure to show all the steps in the process.

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