Nikolsky often includes specific "Control Tasks" at the end of chapters which are very similar to the actual mid-year exam.

Prove a trigonometric identity or simplify a complex fraction involving tantangent cotcotangent

Simplifying expressions using basic identities (e.g., , double angle formulas, and addition formulas). Trigonometric Equations: Solving basic equations like , or those requiring factoring and substitution.

sin2α2cosαthe fraction with numerator sine 2 alpha and denominator 2 cosine alpha end-fraction Find the roots for within a specific interval.

Calculations involving powers with rational exponents and roots of degree

Determining the domain and range of trigonometric functions or identifying properties like parity (even/odd). Sample Task Breakdown Simplification: Compute the value of an expression like 16⋅814the fourth root of 16 center dot 81 end-root or simplify

Ensure you are comfortable converting degrees to radians quickly (