Q. 6 C5.0( 2 Votes )

Solve the following equations :

sin x + cos x = 1

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,


.


In all such problems we try to reduce the equation in an equation involving single trigonometric expression.


{ dividing by √2 both sides}


{ }


{ cos A cos B + sin A sin B = cos (A - B)}


NOTE: We can also make the ratio of sin instead of cos , the answer remains same but the form of answer may look different, when you put values of n you will get same values with both forms


If cos x = cos y, implies x = 2nπ ± y, where n Z


s


.


.


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