# Help with Proving Trigonometric Identities

• chase222
In summary, the person needs help solving two proofs: (sec^2x-1)/(sec^2x) = sin^2x and cos^2x/(1+tan^2x) = cot^2x. They are unsure of how to proceed after simplifying the expressions and are asking for assistance. However, the second problem given may have a mistake. The expert suggests using known trigonometric identities and practicing solving equations mentally to become more familiar with the concepts.
chase222
I need help solving these 2 proofs:

(sec^2x-1)/(sec^2x) = sin^2x
I am not sure what direction to go in. I know the top of the left side could be changed into:
tan^2x/sec^2x, but I don't know what to do after that.

The second one I need help with is:

cos^2x/(1+tan^2x) = cot^2x
I simplified it into:
cos^2x/sec^2x = cos^2x/sin^2x, but I don't know what to do after that. Can you help me get the next few steps of these problems? Thanks!

chase222 said:
(sec^2x-1)/(sec^2x) = sin^2x
I am not sure what direction to go in. I know the top of the left side could be changed into:
tan^2x/sec^2x, but I don't know what to do after that.

remember that tanx=sinx/cosx? try that

chase222 said:
The second one I need help with is:

cos^2x/(1+tan^2x) = cot^2x
I simplified it into:
cos^2x/sec^2x = cos^2x/sin^2x, but I don't know what to do after that. Can you help me get the next few steps of these problems? Thanks!

this one is done. again, remember that cotx=1/tanx, so what is cotx in terms of sin and cos?

chase...u seem to be a small boy just starting to learn math...am i right?

first problem...sec^2 x-1/sec^2 x=sin^2 x...
ie...tan^2 x/sec^2 x=RHS
ie...sin^2 x*cos^2 x/cos^2 x...that is equal to sin^2 x...isnt it?/
and the second problem u have given is wrong...there is some mistake in it...dont worry..trigonometry is easy...just try to create equations urselves...solve most of them using mind...then take ur pen...because u should be learning them like drinking water...so have them in ur fingertips...

## 1. What are trigonometric identities?

Trigonometric identities are mathematical equations that involve trigonometric functions such as sine, cosine, and tangent. They are used to relate the values of these functions to each other and are often used to simplify and solve trigonometric equations.

## 2. Why is proving trigonometric identities important?

Proving trigonometric identities is important because it helps to strengthen our understanding of trigonometry and its applications. It also allows us to manipulate and simplify complex trigonometric expressions, making them easier to solve.

## 3. What is the process for proving trigonometric identities?

The process for proving trigonometric identities involves using algebraic manipulations and the properties of trigonometric functions to transform one side of the equation into the other. This is done step by step, following a set of rules and identities, until both sides of the equation are equal.

## 4. How can I improve my skills in proving trigonometric identities?

To improve your skills in proving trigonometric identities, it is important to have a strong understanding of trigonometric functions, their properties, and identities. Practice solving a variety of problems and familiarize yourself with different techniques for proving identities.

## 5. Are there any shortcuts or tips for proving trigonometric identities?

Yes, there are some tips and tricks that can make proving trigonometric identities easier. These include using Pythagorean identities, working with complex numbers, and using double angle formulas. It is also helpful to simplify expressions and break them down into smaller parts to make the process more manageable.

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