Enter two trigonometric expressions and verify identity by graphical comparison and numerical sampling across domains.
Enter two trigonometric expressions and this tool answers one question: do they describe the same function? It plots both curves on the same axes over the domain you choose, then evaluates the two expressions side by side at a grid of sample points and reports the largest absolute difference between them. The surprise most users hit: a clean match is strong evidence, not a proof. Sampling can never rule out two functions that agree at every sampled point yet differ in between, so a passing result means 'no counterexample found', while a failing one is definitive.
A concrete input and expected output from the current implementation.
Input
LHS: sin(x)^2 + cos(x)^2 RHS: 1 domain: [0, 2*pi]
Expected output
Every sampled point matches: the largest |LHS - RHS| is about 1e-16, at the limit of double-precision arithmetic, and the two curves overlay exactly across [0, 2*pi]. Verdict: the identity holds on this domain.
sin(x)^2 + cos(x)^2 = 1 is the Pythagorean identity, true for every real x. Floating-point evaluation of both sides lands within 1e-16 of equality at every sample, so both the graphical and the numerical checks return the tool's cleanest possible pass.
Each expression is parsed as a function of x: sin(x), cos(x), tan(x) and the other standard trig functions are available, powers use ^, and multiplication uses *. The tool then evaluates both expressions across your chosen domain, draws the two curves on one set of axes, and computes LHS - RHS at every point of its sampling grid, keeping the largest absolute difference and the x value where it occurs.
The comparison is numerical. Each sample is a floating-point evaluation, and values that agree within a small tolerance count as a match, so the verdict depends on the grid and the tolerance. Two distinct functions can coincide at every sampled point and diverge between them, and agreement over a bounded interval says nothing about x outside it. A symbolic proof engine would be needed to establish equality for all x.
No. The check is finite sampling over a bounded interval, which can only produce a counterexample, never rule all of them out. A match means no disagreement appeared at hundreds of points, which is strong evidence but not a proof. To establish an identity for every x, you still need an algebraic derivation.
Start at the point of largest difference. Usually one of three things is wrong: the expressions differ where one is undefined (the poles of tan(x) in tan(x)*cos(x) = sin(x)), the input was parsed differently than you intended, or the domain choice crosses a point where a rewritten form changes behavior. Compare the two curves there.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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