Final answer:
The question requests simplification of trigonometric expressions using identities and ensuring that dimensions are consistent, especially when applied to physics.
Step-by-step explanation:
The student's question involves expressing trigonometric expressions in terms of sine and cosine and simplifying them. For example, when the question mentions cos 2θ as cos² θ - sin² θ, it's referring to the double-angle identity for cosine. Furthermore, expressions like sin 20 and the usage of sine and cosine functions in physics equations, such as in the context of momentum, can be simplified by applying trigonometric identities. The sine and cosine functions are also crucial in understanding concepts such as the law of sines and the law of cosines in triangles. Trigonometric identities help to simplify and manipulate equations, ensuring that dimensions are consistent, particularly in physics where dimensionless quantities are often required within trigonometric functions.