Trig Identities Calculator

Introduction to Trig Identities Calculator:

Trig identities calculator is an online tool that helps you to solve the trigonometric function problem using trigonometric identities. It is used to simplify the process of solving complex trigonometric functions which cannot be solved by another process except the trig identities function.

If you are facing trouble in solving the trigonometric identities function then you need a reliable tool like our solving trigonometric identities calculator. It gives you an immediate solution without any error even if you give complicated trig identities function problems.

What is a Trig Identity?

Trig identity is a process that is used to easily find the solution of trigonometric functions especially when they cannot get a solution with other mathematical methods. It is a basic concept that makes the calculation process of trigonometric functions smooth.

Trigo identify function has various types like basic trig identity, sum and difference identity function, half angle trig identity, and double angle identity which is used in many mathematical and engineering concepts.

Formula of Trig Identities:

The basic trig identities for the trigonometric equation used by the trig identities calculator are described below. The square sum of cosine and sine function is equal to,

$$ cos^2 \theta + sin^2 \theta \;=\; 1 $$

The relationship between tangent and secant function is,

$$ 1 + tan^2 \theta \;=\; sec^2 \theta $$

The relationship between cotangent and cosec function is,

$$ cot^2 \theta + 1 \;=\; csc^2 \theta $$

How to Calculate Trig Identities?

In the calculation of trigonometric identities, the trig identity calculator uses systematic steps to simplify given trigonometric expressions. Here is a step-by-step guide to help you with the working process of trigonometric identities function.

Step 1:

Identify the trigonometric expression that you need to simplify.

Step 2:

Choose the basic identities as per your given trigonometric function and apply it for simplification.

$$ cos^2 \theta + sin^2 \theta \;=\; 1 $$

$$ 1 + tan^2 \theta \;=\; sec^2 \theta $$

$$ cot^2 \theta + 1 \;=\; csc^2 \theta $$

Step 3:

Add the identity value in the given trigonometric function.

Step 4:

Then combine like terms and simplify the expression by using algebraic techniques to reduce it into the simplest form.

Practical Example of Trig Identities:

The trig identities calculator is used to determine the trig identities easily but for understanding the calculation process manually you have to know its steps. So an example with step by step solution is given below,

Example: prove that

$$ tan \theta + cot \theta \;=\; sec \theta csc \theta $$

Solution:

We have to show that tan and cot is equal to,

$$ tan \theta + cot \theta \;=\; sec \theta csc \theta $$

For this take,

$$ tan \theta + cot \theta $$

We can write it as,

$$ tan \theta \;=\; \frac{sin \theta}{cos \theta} $$

$$ cot \theta \;=\; \frac{cos \theta}{sin \theta} $$

Put these values in the given equation,

$$ tan \theta + cot \theta \;=\; \frac{sin \theta}{cos \theta} + \frac{cos \theta}{sin \theta} $$

Multiply and divide the denominator,

$$ \frac{sin \theta}{cos \theta} . \frac{sin \theta}{sin \theta} + \frac{cos \theta}{sin \theta} . \frac{cos \theta}{cos \theta} $$

Take the common denominator to solve the equation,

$$ =\; \frac{sin^2 \theta + cos^2 \theta}{cos \theta sin \theta} $$

Apply the trig identity,

$$ cos^2 \theta + sin^2 \theta \;=\; 1 $$

$$ \frac{1}{cos \theta sin \theta} $$

It can be written as,

$$ \frac{1}{cos \theta} . \frac{1}{sin \theta} $$

Put these values in the above equation,

$$ \frac{1}{cos \theta} sec \theta $$

$$ \frac{1}{sin \theta} csc \theta $$

Therefore the solution is,

$$ =\; sec \theta csc \theta $$

How to Use the Trig Identities Calculator?

The trigonometric identities calculator has a simple design that enables you to use it to calculate the trig function identities questions easily.

Before adding the trig function as an input value in the trig identity calculator, you must follow some of our guidelines. These guidelines are:

1. Enter your trig identity equation problem in the input field.
2. Recheck your trig identities problem before hitting the calculate button to start the calculation process of the trigonometry proof solver.
3. Click on the “Calculate” button to get the desired result of your given Trig identities question.
4. If you want to try out our trig identity solver for the first time then you can use the load example.
5. Click on the “Recalculate” button to get a new page for solving more trig identity problems to get solutions.

Output of Trigonometric Identities Calculator:

The identity trig calculator gives you the solution to a given trig identity problem when you add the input into it. It provides you with solutions to the trig function problem. It may contain the following:

• Result Option:

You can click on the result option and then verify the identity calculator provides you with a solution for the trig identities questions.

• Possible Step:

When you click on the possible steps option it provides you with the solution of trig identities problems in detail.

Uses of Trig Identity Calculator:

The trig proof solver has many uses that you obtain whenever you use it to calculate trig identities for finding the trigonometric function solutions. These features are:

• The verify the identity calculator is an easy-to-use tool that can operate through electronic devices like laptops, computers, mobile, tablets, etc with the help of the internet.
• The identity trig calculator is a free tool so you can use it to find the trig function problems.
• Our tool saves the time and effort that you consume in doing lengthy calculations of trigonometric identity function problems.
• You can use the trig identity solver for practice so that you get in-depth knowledge about this method.
• It is a trustworthy tool that provides you with accurate solutions of trig identities problems whenever you use it to get a solution.
• The trig identities calculator provides you solutions to trigonometric identities function questions with a complete process in a stepwise method for a better understanding.