Final answer:
The analytical method is used to simplify trigonometric expressions, which predominantly involves utilizing trigonometric identities such as the double angle formulas, Pythagorean theorem, Law of Sines, and Law of Cosines.
Step-by-step explanation:
The method used to simplify trigonometric expressions is referred to as the analytical method. This method commonly involves the use of trigonometric identities and sometimes the Pythagorean theorem, to rewrite expressions in a simpler form or to solve for unknowns. Trigonometric identities such as the double angle identities, for example, sin(2θ) = 2sin(θ)cos(θ) or cos(2θ) = cos2(θ) - sin2(θ), allow expressions to be written in alternative forms. The analytical method is more accurate than graphical methods because it avoids approximation errors that could occur when drawing or measuring. To solve trigonometric problems, we often rely on additional theorems such as the Law of Sines and the Law of Cosines, which relate the sides and angles of triangles, providing powerful tools to analyze and solve for unknown quantities in trigonometry.