Final answer:
The question relates to trigonometric identities and functions in Mathematics, specifically double angle identities like cos(2x), and combining polynomial with trigonometric functions.
Step-by-step explanation:
The student's question pertains to trigonometry, specifically trigonometric identities and functions. The use of sin and cos denotes sine and cosine functions, which are fundamental in understanding angles and their properties in triangles and periodic functions. The equation cos(2x) = cos^2(x) - sin^2(x) represents a double angle identity for cosine, which simplifies the expression for the cosine of twice an angle.
In more complex examples, these identities are essential for simplifying expressions and solving trigonometric equations. The function f(x)=2x^2+tan(x) combines polynomial and trigonometric functions, indicating the need to understand both algebra and trigonometry for analysis. It's important to note that the identities provided (sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos^2(θ) - sin^2(θ), etc.) are pivotal in simplifying trigonometric expressions and solving equations.