Q. 1 D4.5( 2 Votes )

Find the general solutions of the following equations :


Answer :


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 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.


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