How to use this calculator
- Enter or choose left side.
- Enter or choose right side.
- Enter or choose angles in.
- Enter or choose show both sides at x =.
- The verdict updates as you type. Use Copy result or Share to keep it.
Method
Evaluate L(x) and R(x) at 400 angles spread over two full turns (avoiding multiples of 90°); the identity fails if |L − R| > 10⁻⁹ × max(1, |L|, |R|) at any of them
- L(x), R(x)
- the two sides you type
- x
- the angle, in degrees or radians as chosen
Worked example
- At x = 60°: cos 120° = −0.5.
- Right side: 1 − 2 × sin²60° = 1 − 2 × 0.75 = −0.5.
- The same comparison at 400 angles finds no difference larger than floating-point rounding.
cos 2x = 1 − 2 sin²x agreed at every one of the 400 test angles, as expected for this double-angle identity.
What the result means
A counterexample settles the question: the expressions are not identical. Agreement at every test angle is convincing evidence but not a proof; to prove an identity, transform one side into the other with known identities.
Assumptions and limits
- In degree mode, x and every trig function argument are in degrees, and pi stands for 180°.
- Angles where either side is undefined (for example tan at 90°) are skipped.
- Numerical testing cannot prove an identity, and cannot detect differences smaller than about 10⁻⁹ of the values.
- Inverse trig functions and hyperbolic functions are not supported.
Questions
How do I write sin squared?
Type sin^2(x) or sin(x)^2. Write products with or without *: 2sin(x)cos(x) works.
Why is this not a proof?
Two different functions can agree at many points. The checker samples 400 angles, which catches every common mistake, but a formal proof uses algebraic steps.