Question

Principal solution and general solution

Answer 1

Principle solution of trigonometric equation restrict the solution in the Range 0 <= x < 2π.

The expression involving integer ’n’ which gives all solutions of a trigonometric equation is called general solution

To derive the general solution , we use the periodicity of trigonometric functions .

Period of Sin(x) = 2π
Cos(x) = 2π
Tan(x)=π

For general solution , we also use some Standard results.

1) if Sin(x) = Sin (y) => x = nπ +(-1)^n * y , where n is an integer.

2) if Cos(x) = Cos(y) => x = 2nπ y + - y , where n is an integer.

3) if x & y are not multiple of π/2

Then Tan(x) = Tan(y) => x = nπ + y , where n is an integer .