Thread locked. A related question is posted in the Precalc Homework section.Callumnc1 said:
Trigonometric identities are used to simplify and manipulate trigonometric expressions, making them easier to solve and understand. They are also used in various branches of mathematics, physics, and engineering.
There is no specific rule for determining which identity to use. It often depends on the given expression and what you are trying to solve for. Familiarity with a variety of identities can be helpful in choosing the most appropriate one.
Yes, trigonometric identities can be proven using algebraic manipulations and the fundamental definitions of trigonometric functions. However, some identities may be more challenging to prove than others.
Some common strategies include using Pythagorean identities, sum and difference formulas, double angle formulas, and converting trigonometric functions into their reciprocal or quotient forms.
Practice and familiarity are key to remembering trig identities. It can also be helpful to understand the underlying concepts and connections between different identities. Creating flashcards or using mnemonic devices can also aid in memorization.