Find all solutions of the equation in the interval [0, 2π). cos x + sin x tan x = 2

The solutions of the equation in the interval [0,2π )

                    ={   }

General solution    θ = 2 nπ +α

                                θ =  

Step-by-step explanation:

Step(i):-

Given equation

                      cos x + sin x tan x = 2

               ⇒      

    On simplification , we get

              ⇒    

we know that trigonometry formula

now we get

⇒        

⇒         cos x = cos 60°

Step(ii):-

General solution of cosθ = cosα

General solution    θ = 2 nπ +α

                               θ = 2 nπ +60°

                                θ =  

put n = 0 ⇒ θ = 60°

Put n =1 ⇒  θ = 360°+60°= 420°

.....and so on

The solutions of the equation in the interval  =

Final -

The solutions of the equation in the interval [0,2π )

                    ={   }

General solution    θ = 2 nπ +α

                                θ =  

7

step-by-step explanation:

3

step-by-step explanation: