Trigonometric Identity Calculator
🧮 Trigonometric Identity Calculator – Verify Trig Identities Instantly
Are you a student or teacher struggling to verify trigonometric identities like
sin²(x) + cos²(x) = 1 or 1 + tan²(x) = sec²(x)?
With our Trigonometric Identity Calculator, you can now instantly verify these identities with any angle in degrees.
Whether you’re preparing for exams or teaching trigonometry, this tool will help you simplify complex expressions and confirm trigonometric truths in seconds.
🎯 What is a Trigonometric Identity?
A trigonometric identity is a mathematical equation involving trigonometric functions that is always true for any value of the angle (for which both sides are defined).
Some of the most important and commonly used trig identities are:
- sin²(x) + cos²(x) = 1
- 1 + tan²(x) = sec²(x)
- 1 + cot²(x) = cosec²(x)
These identities form the foundation of higher-level trigonometry, calculus, and geometry.
✅ Features of the Trigonometric Identity Calculator
- 🔢 Verifies multiple identities:
– sin²(x) + cos²(x) = 1
– 1 + tan²(x) = sec²(x)
– 1 + cot²(x) = cosec²(x) - 🧠 Takes input in degrees
- ⚡ Instantly checks if the identity is true or false
- 📱 Fully responsive – Works on desktop, mobile, and tablets
- 🧮 Uses precise JavaScript calculations
- 💡 Great for students, teachers, and competitive exam aspirants
⚙️ How to Use the Trigonometric Identity Calculator?
- Enter an angle in degrees (like 30°, 45°, or 60°).
- Select an identity from the dropdown.
- Click on the “Verify Identity” button.
- See if the identity is TRUE or FALSE, along with LHS and RHS values.
📚 Behind the Scenes – How It Works
This tool uses JavaScript’s Math functions to calculate:
- sin²(x), cos²(x), tan²(x), cot²(x), sec²(x), and cosec²(x)
- Then it checks if LHS ≈ RHS (allowing for floating-point precision up to 6 decimal places)
It’s perfect for students who want to check their manual solutions, or teachers looking to demonstrate proofs live in class.
🧠 Example Calculations
| Identity | Angle | LHS Value | RHS Value | Result |
|---|---|---|---|---|
| sin²(x) + cos²(x) = 1 | 60° | 1.000000 | 1.000000 | ✅ TRUE |
| 1 + tan²(x) = sec²(x) | 45° | 2.000000 | 2.000000 | ✅ TRUE |
| 1 + cot²(x) = cosec²(x) | 30° | 4.000000 | 4.000000 | ✅ TRUE |
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🙋 Frequently Asked Questions (FAQs)
Q1. Can this calculator prove all trigonometric identities?
No, it currently supports the three primary Pythagorean identities. More identities will be added soon.
Q2. Is this calculator free to use?
Yes! It’s completely free and requires no sign-up.
Q3. Does it work with radians?
No, it works with degrees only to make it easier for students.
Q4. Is this calculator accurate?
Yes, it uses precise math functions and compares both sides with a tolerance for floating-point rounding.
🏷️ Meta Title & Description for SEO
Meta Title (60 characters):
Trigonometric Identity Calculator – Verify sin², tan², cot²
Meta Description (120 characters):
Verify trigonometric identities like sin²(x) + cos²(x) = 1 and more. Use our free identity calculator for instant results.
🏁 Final Thoughts
Trigonometry can be tricky—but not when you have smart tools at your fingertips.
Our Trigonometric Identity Calculator helps you learn faster, solve better, and verify instantly.
So next time you’re solving a trigonometry problem, give our calculator a spin. It could save you time, effort, and errors!
