Question

find the general solution of sin x + cos x = 1​

Answer 1

Answer:

Step-by-step explanation:

We have,

cosx+sinx=1

⇒2

​1​cosx+2

​1​sinx=2

​1​ ....[Dividing both sides by 2

​]

⇒cos4π​cosx+sin4π​sinx=2

​1​

⇒cos(x−4π​)=cos4π​

∴x−4π​=2nπ±4π​, where n∈I

⇒x=2nπ±4π​+4π​, where n∈I

⇒x=2nπ+4π​+4π​,2nπ−4π​+4π​, where n∈I

⇒x=2nπ+2π​,2nπ, where n∈I

x=(4n+1)2π​,2nπ, where n∈I

This is the required general solution.

Answer 2

Step-by-step explanation:

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