Final answer:
The query is about trigonometry, focusing on trigonometric functions and identities used in calculating angles and solving geometry problems.
Step-by-step explanation:
The student's question appears to be related to trigonometry, specifically the use of trigonometric functions like sine, cosine, and tangent, as well as the application of trigonometric identities and their use in solving problems involving angles. Examples from the provided information include applications of the sine and cosine laws in triangles and transformations of trigonometric expressions, such as using the double angle formulas.
For instance, one of the identities mentioned is cos 2θ = cos² θ - sin² θ = 2 cos² θ - 1 = 1- 2 sin² θ, which is known as the cosine double angle formula and can be used to derive several other important trigonometric relationships.