Solve the following equations :

cos x + sin x = cos 2x + sin 2x


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,


cos x + sin x = cos 2x + sin 2x


cos x – cos 2x = sin 2x – sin x


{ sin A - sin B =





Hence,


Either,



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



where m,n ϵ Z ….ans


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