Custom Simplifier
Pattern simplification completed.
| Before | After | Rule |
|---|---|---|
| tanx · cosx | sinx | Exact identity match |
Examples
Step-by-Step Simplification
Step 1: Read the custom expression
infoThe calculator normalizes powers, signs, and function notation.
Step 2: Exact identity match
successA known trig identity was applied.
Trigonometric Simplification Notes
Trigonometric simplification uses known identities to change an expression without changing its value. The most common starting point is the Pythagorean identity. It connects sine and cosine through the equation sin²x plus cos²x equals one. From that single rule, tangent, secant, cotangent, and cosecant identities can also be built by division.
Another useful method is rewriting everything in sine and cosine. This often turns complicated expressions into ordinary algebraic fractions. After that, factors may cancel, common denominators may combine, and Pythagorean expressions may appear. This calculator follows that workflow in several tools.
Double-angle, half-angle, power-reducing, product-to-sum, and sum-to-product identities are transformation rules. They are especially useful when an expression contains products, high powers, or angle multiples. These forms help students compare two sides of an identity and choose a useful proof path.
A numeric check is included for quick testing. It evaluates both expressions at a selected angle. Matching values suggest that the expressions may be equivalent, but a numerical check is not a complete proof. A proof must show that both expressions match for every valid angle in the domain.