Solving Trigonometric Identities (A bit Hard)

OT(x)CSC(x)In summary, the conversation discusses solving a trigonometric identity and the steps taken to reach the solution. The focus is on finding a common denominator and cancelling terms to simplify the equation to equal COT(x)CSC(x). The speaker expresses gratitude for the help and mentions making a mistake while solving the problem.
  • #1
cmhabs94
3
0
Alright, well I am having a difficult time getting these equations to equal out! I keep hitting trouble and have hit a road block.

Here is the problem...

csc(x)+cot(x) = cot(x)csc(x)
tan(x)+sin(x)

I am just going to work on the LEFT PART of the equation.

1 + cos(x)
sin(x) sin(x)
ALL OVER
sin(x) + sin(x)
cos(x)

so...
1 + cos(x) / sin(x) * cos(x) / sin(x) + sin(x)cos(x)

simplifying the bold leads to...

1 + cos(x) / sin(x) * cos(x) / sin(x)(1+cos(x))

I am stuck here, particular getting the common denominator and then simplyfing it out to equal cot(x)csc(x)

Any help would be appreciated, thanks.
 
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  • #2
Hello,
I believe you are on the right track with this solving trigonometric identities.

(1+Cos(x))/Sin(x) * Cos(x)/(Sin(x) + Sin(x)Cos(x))

Factor out the Sin(x) on the bottom and cancel the (1+Cos(x)) term (Top and Bottom)

(1+Cos(x))/Sin(x) * Cos(x)/(Sin(x)*(1+Cos(x))

thus,

1/Sin(x) * Cos(x)/Sin(x) = CSC(x)COT(x)
 
  • #3
Thank you so much! I kept going over that problem for about 30 mins; so focused on getting a common denominator that I forget to cross cancel! Ahh, I hate stupid mistakes.

Thanks,
- C
 

What are trigonometric identities?

Trigonometric identities are mathematical equations involving trigonometric functions (such as sine, cosine, and tangent) that are true for all values of the variables involved.

Why is solving trigonometric identities considered difficult?

Solving trigonometric identities can be challenging because it requires a deep understanding of the relationships between trigonometric functions and how they can be manipulated algebraically. It also often involves multiple steps and requires a lot of practice to master.

What are some strategies for solving trigonometric identities?

There are several strategies that can be helpful when solving trigonometric identities. These include using the fundamental trigonometric identities, using algebraic manipulation, using Pythagorean identities, and applying trigonometric identities to simplify the equation.

What are some common mistakes to avoid when solving trigonometric identities?

Some common mistakes to avoid when solving trigonometric identities include forgetting to use parentheses when substituting values, making sign errors, and not simplifying the equation fully before trying to solve it. It is also important to be careful when dealing with inverse trigonometric functions.

How can I improve my skills in solving trigonometric identities?

The best way to improve your skills in solving trigonometric identities is to practice regularly and familiarize yourself with the fundamental trigonometric identities. Additionally, seeking help from a teacher or tutor and working through practice problems can also be beneficial.

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