Identities and equations

Trigonometric identities, used to simplify or solve equations, are essential to Core Pure Mathematics 2. This includes the Pythagorean identity (sin^2(x) + cos^2(x) = 1) and the double-angle identities (sin(2x) = 2sin(x)cos(x), cos(2x) = cos^2(x) - sin^2(x)).
Another vital concept is the hyperbolic functions and their related identities. Understand sinh, cosh and tanh functions, as well as their respective squared identities.
Know the origin of these identities, such as Euler’s formula for complex numbers. This understanding will help when dealing with more complex, compound trigonometric equations.
Complex numbers play a significant role in these identities and equations. Be aware of the real and imaginary parts of a complex number (Re(z) and Im(z)) and their geometric representations in the Argand diagram.
Polynomials and their equations are also a Core Pure Mathematics 2 topic. Understand what defines a polynomial, its degree, and the factor and remainder theorems.
Learn how to decompose fractions into partial fractions, an essential tactic to simplifying the integration of certain functions.
Grasp the concept of roots of unity, specifically the nth roots of unity. Understand De Moivre’s theorem and the role it plays in solving polynomial equations.
Attain mastery on solving trigonometric and hyperbolic equations, covering simple cases up to more complex ones involving multiple angles or multiple functions.
Remember, the identities in this part of the subject are normally used together with other aspects of mathematics like differentiation and integration. Make sure to not only understand these identities, but also how and when to apply them in different scenarios.
Practice regularly from a variety of sources to gain exposure to a range of problems. This will boost your confidence and your ability to handle different types of questions.