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 1st and 4th quadrant.
While giving 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 / 6
∴ x = 2nπ ± ,where n ϵ Z
Thus, x gives the required general solution for the given trigonometric equation.