Find the general solutions of the following equations :

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ⁿy, where n ∈ Z.

• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.

• tan x = tan y, implies x = nπ + y, where n ∈ Z.

Given,

We know that sec x and cos x have positive values in the 1^st and 4^th quadrant.

While giving a solution, we always try to take the least value of y

both quadrants will give the least magnitude of y.

We can choose any one, in this solution we are assuming a positive value.

⇒

If cos x = cos y then x = 2nπ ± y, where n ∈ Z.

For above equation y = π / 4

∴ x = 2nπ ± ,where n ϵ Z

Thus, x gives the required general solution for the given trigonometric equation.