Choose a proof mode
Select a strategy, load an example, or enter your own identity values.
About proving trigonometric identities
What a proof should show
A trigonometric identity proof must show that two expressions are equivalent for every angle where both sides are defined. A strong proof changes one side step by step until it becomes the other side.
Useful proof strategies
Common strategies include rewriting all functions in sine and cosine, using reciprocal identities, creating common denominators, factoring expressions, multiplying by conjugates, and applying Pythagorean identities.
Why numeric checks help
A numeric check does not replace a formal proof. It helps catch typing errors and undefined values. If many samples fail, the identity may be false or the expression may need a different domain.
Domain restrictions
Every identity has a shared domain. Denominators cannot be zero, reciprocal functions need nonzero sine or cosine values, and half-angle signs must match the correct quadrant.
FAQs
What does this calculator prove?
It proves selected trigonometric identity patterns and checks custom identities numerically with safe sample angles.
Can it prove any typed identity?
It can numerically test typed identities, but unrestricted symbolic proof is limited to the built-in proof templates.
Why should I start with one side?
Working on one side avoids circular reasoning. The proof ends when that side becomes the other side.
What is a conjugate proof?
It multiplies by a matching expression such as 1 − sinθ to create a difference of squares.
Why are domain restrictions important?
Some transformations divide by expressions that may equal zero. The proof is valid only where both sides are defined.
Can I use radians?
Yes. Angle fields support degree or radian mode, including pi-style entries like pi/6.
What does the custom checker support?
It supports sin, cos, tan, sec, csc, cot, sqrt, abs, pi, x, and simple exponent notation.
Is numeric checking a proof?
No. It is evidence and a debugging tool. Formal proof needs algebraic identity transformations.
Can I print the proof?
Yes. Use the Print / PDF button to save the steps.
Can I download the proof table?
Yes. Use Download CSV to export the result table.