About The Prove Trig Identity Calculator
A trigonometric identity looks simple when both sides match. The work becomes harder when the expression is long. This calculator helps you compare two sides with a careful numerical proof check. It does not replace a written proof. It gives strong evidence, rewrite hints, and domain warnings.
The tool tests both expressions at many safe sample values. It converts supported functions into a controlled expression. Then it compares the left side and right side. A very small difference means the identity is likely true on the tested domain. A large difference suggests the statement is not an identity.
Use standard identities before you trust any result. Reciprocal rules change secant, cosecant, and cotangent. Quotient rules change tangent and cotangent. Pythagorean identities are also common. The calculator lists these formulas below, so you can connect the result with a written solution.
Domain is important. Some values make tangent, secant, cosecant, or cotangent undefined. Division by zero can also happen. The checker skips unsafe points and reports how many valid tests were used. If too many points fail, inspect the original expressions.
For best results, enter one variable only. Use x as the default variable. Put powers with the caret sign. Write sin(x)^2 instead of sin2x. Use clear parentheses around fractions and products. This keeps the parser simple and safer.
The tolerance setting controls strictness. A smaller tolerance is harder to pass. A larger tolerance is more forgiving when decimals are involved. The default value works well for most classroom identities.
The CSV export is useful for spreadsheets. The PDF export is useful for reports. Both exports include the compared sides, test status, maximum difference, and notes. Teachers can save examples for lessons. Students can keep practice records.
Always finish with algebra. Use the calculator to find confidence. Then write transformations step by step. Start from one side. Apply a valid formula. Simplify until it equals the other side.
Advanced options help with mixed lessons. You can choose radians or degrees, change sample density, and set a custom variable name. These controls make the checker useful for basic examples and tougher identities. Keep notes, compare trials, and review mistakes after each test. This habit builds cleaner proofs over time slowly.