▸Angle 45°: all nine power-reduced values computed.
- cos(2x) = 0.000000 is the key intermediate value. Every identity below is built from it.
- sin²(45°) = 0.500000, cos²(45°) = 0.500000. Their sum equals 1, confirming the Pythagorean identity.
- The fourth-power reductions sin⁴(x) = 0.250000 and cos⁴(x) = 0.250000 are useful in calculus when integrating trigonometric expressions raised to the fourth power.
- Power-reducing formulas are the standard first step when integrating even powers of sine or cosine, because the resulting single-frequency cosine terms integrate directly.
Next stepTo integrate sin²(x) or cos²(x), substitute the reduced form directly: the double-angle cosine term integrates to sin(2x)/2, which is straightforward by the chain rule.