Trigonometric equation: An equation having trigonometric functions is called a trigonometric equation.
Ex : sin θ = 1
sin θ + cos θ =1
tan θ = 1
Trigonometric identity : A trigonometric identity is also an equation which gets satisfied by any value of the unknown quantity.
Ex : sin2θ + cos2θ=1
Key Point: A trigonometric equation is satisfied by finite or infinite specific values of the unknown quantity not by any value of the unknown quantity.
Solution of a trigonometric equation: There are two types of solutions of a trigonometric equation:
I. Principal solution: A solution in which the values of the unknown quantity belong to the interval [0,2π] is called a principal solution.
II. General solution: A solution in which there are infinite values of the unknown quantity is called a general solution.
Important results :
I. sin θ = 0 ⇒ θ = nπ II. cos θ = 0 ⇒ θ = (2n+1)π/2 III. tan θ = 0 ⇒ θ = nπ