Mathematics

Trigonometric identities are equations that hold for all values in their domain—they're not just coincidences for special angles. The key is recognizing which relationships come directly from the Pythagorean theorem and the definitions of sine and cosine on the unit circle. Test any candidate identity by checking whether it follows logically from $\sin^2 A + \cos^2 A = 1$ or from the ratio definitions, rather than plugging in specific angles.

Trigonometric identities are equations that hold for all values in their domain—they're not just coincidences for special angles. The key is recognizing which relationships come directly from the Pythagorean theorem and the definitions of sine and cosine on the unit circle. Test any candidate identity by checking whether it follows logically from $\sin^2 A + \cos^2 A = 1$ or from the ratio definitions, rather than plugging in specific angles.