Calxsolver
Trigonometry

Trig Identity Verifier

Enter the two sides of a candidate identity as expressions in x. The verifier evaluates both at a battery of test points scattered across (0, 2π); if they agree everywhere to within tolerance the identity is reported as verified, otherwise a counterexample is shown.

Trig Identity Verifier

Check whether LHS = RHS as an identity by numeric sampling.

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Frequently asked questions

Is a verified identity really a proof?

No — agreement at many test points is strong empirical evidence but not a formal proof. A purely symbolic identity proof requires manipulating both sides through known identities; that is a separate, much harder task.

Why use sampling instead of symbolic manipulation?

Trig identity simplification is genuinely hard and not unique; numeric sampling catches almost every real-world identity mistake quickly and reliably, and it provides a concrete counterexample when the candidate fails.

What sample points are used?

About a dozen values spread across (0, 2π), avoiding obvious singularities. The tolerance is relative so the test scales with the magnitude of the expressions.

Related solvers

Right Triangle Solver Solve a right triangle from its two legs. Trig Function Evaluator Evaluate sin, cos, tan, csc, sec or cot of an angle. Pythagorean Theorem Find the missing side of a right triangle. Law of Cosines Solve a triangle from two sides and the included angle. Law of Sines Solve a triangle from two angles and a side. Angle Converter Convert degrees and radians, with reference angle. Trig Equation Solver Solve sin(x) = c, cos(x) = c, tan(x) = c (and reciprocals) with general solution. Cartesian to Polar Coordinates Convert (x, y) to (r, θ), reporting θ in both degrees and radians. Polar to Cartesian Coordinates Convert (r, θ) to (x, y), accepting θ in degrees or radians.