Math, asked by gokilavani9394, 10 months ago

The number of roots of equation x+2tanx=pi/2 in the interval[0,2pi]l

Answers

Answered by amitnrw
6

Three roots of Equation  in the  interval[0,2π] for x  + 2Tanx  = π/2

Step-by-step explanation:

x  + 2Tanx  = π/2

2Tanx = π/2 - x

Case 1 : when    x lies between 0 to π/2

=> π/2 - x  is + ve

2Tanx   is also +ve  between 0 to π/2

one function is increasing while other is decreasing

so one value will satisfy between 0 to π/2

Case 2 : when    x lies between π/2 to π

=> π/2 - x  is - ve

2Tanx   is also -ve  between π/2 to π

so one value will satisfy between 0 to π/2

Case 3 : when    x lies between π to 3π/2

=> π/2 - x  is - ve

But 2Tanx   is +ve  between π to 3π/2

so no such value

Case 4 : when    x lies between 3π/2 to 2π

=> π/2 - x  is - ve

2Tanx   is also -ve  between 3π/2 to 2π

so one value will satisfy between 3π/2 to 2π

so three such value exist for x  in the interval[0,2π]

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