Trigonometric equations are equations involving trigonometric functions like sine, cosine, tangent, etc., where the goal is to find the values of the variables that satisfy the equation.

Trigonometric equations can be solved using various techniques, including algebraic manipulation, trigonometric identities, factoring, substitution, and the use of inverse trigonometric functions.

Principal solutions are solutions within a specified interval, typically [0, 2π) or [0°, 360°) for angles measured in radians and degrees, respectively. These solutions represent the primary or fundamental angles satisfying the equation.

General solutions include all possible solutions to a trigonometric equation, accounting for the periodic nature of trigonometric functions. They are expressed as a principal solution plus integer multiples of the period of the trigonometric function.

To verify the validity of a solution, substitute it back into the original equation and ensure it satisfies the equation within the given domain or interval.

Common trigonometric identities include Pythagorean identities, reciprocal identities, quotient identities, cofunction identities, sum and difference identities, and double-angle identities.

Yes, trigonometric equations can have multiple solutions within a given interval due to the periodic nature of trigonometric functions. It's important to consider all possible solutions when solving these equations.

Inverse trigonometric functions (e.g., arcsin, arccos, arctan) are used to find angles that satisfy trigonometric equations. Inverse trigonometric functions "undo" the trigonometric functions, allowing us to solve for the angle values.