I proving two Trig identities

In summary, the conversation discusses solving two trigonometric equations by changing the terms into sine and cosine and simplifying. The important points to remember are to combine fractions and use the trig identity tanx=sinx/cosx. The conversation also mentions using the Pythagorean identity to solve for 1+cot^2x=csc^2x in the first equation.
  • #1
xxiangel
5
0
1. Cos x (sec x + cos x csc^2 x) = csc^2 x

I got as far as this... 1 + cos^2 + cos/sin^2 = csc^2

2. tan x(sin x + cot x cos x) = sec x
 
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  • #2
1. Change everything on the left into terms of cos and sin. Then distribute the cosx, after that try to combine anything you can, change anything you can to tanx, etc.

2. Again, change everything you can into sin and cos first, then distribute.

A few of the most important things to keep in mind are, when you are done with simplifying things and whatnot, if something is a fraction, combine the terms. In such trig identities, one of the most used basic definitions is tanx=sinx/cosx
 
Last edited:
  • #3
xxiangel said:
I got as far as this... 1 + cos^2 + cos/sin^2 = csc^2
Well, you made a mistake somewhere. Substitute in some random angle and you can see that this is not true.
 
  • #4
hey you, i got this
cosX(secX+cosXcsc^2X)=csc^2x
just solve the left side
cosX[(1/cosX)+(cosx/sin^2X)]=csc^2X
then multiply ,so...
cosX(1/cosX)+cosX(cosX/sin^2X)=csc^2X
1+cot^2X=csc^2X
since 1+cot^2X one of the trig identity which equals
to csc^2X, problem solved
 
  • #5
For the future, mrtkawa, have the original poster attempt his/her own work instead of providing the full solution.
 
  • #6
I was able to solve this till 1+cot^2 = Csc^2 , but do you just use pythagorean identity to fine the identity or what? How are these two equal?
 
  • #7
for 2.

change everything to cos and sin

SinX/CosX[SinX + CosX/SinX(CosX)] = 1/Cosx

work inside the bracket now.

Cosx/sinx(cosx) = cos^2x/sinx
SinX + Cos^2x/Sinx Now get common denominators
you should notice something and be able to work from there.
 

What is the purpose of proving two Trig identities?

The purpose of proving two Trig identities is to show that they are equivalent forms of each other. This means that they can be rearranged and simplified into the same expression, which can be useful in solving mathematical problems.

What are the basic steps for proving two Trig identities?

The basic steps for proving two Trig identities are: 1) Start with one side of the identity and use algebraic and trigonometric properties to manipulate it into the other side; 2) Work with one side of the identity at a time, using known identities and properties to make substitutions and simplify the expression; 3) Continue manipulating both sides until they are equal, proving the identity.

How can I determine which side of the identity to start with?

It is usually recommended to start with the more complex side of the identity, as it can be easier to simplify and manipulate into the simpler side. However, sometimes it may be more beneficial to start with the simpler side depending on the problem and your own preference.

What are some common identities that can be used when proving Trig identities?

Some common identities that can be used when proving Trig identities include: Pythagorean identities, double angle identities, half angle identities, sum and difference identities, and reciprocal identities. It is important to have a good understanding of these identities in order to successfully prove Trig identities.

How can I check if my proof of a Trig identity is correct?

One way to check if your proof is correct is to substitute values for the variables in the identity and see if both sides result in the same value. Another way is to check with a calculator or online tool that can verify the identity. It is also helpful to double check your work and make sure all steps are accurate and follow the rules of algebra and trigonometry.

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