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Prove that the least positive value of x...

Prove that the least positive value of `x ,` satisfying `tanx=x+1,` lies in the interval `(pi/4,pi/2)`

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Let f(x) = tan x and g(x) = x + 1, which could be shown as follows.

From the above the figure, tan x = x + 1 has infinitely many solutions, but the least positive value of `x in ((pi)/(4), (pi)/(2)).`
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CENGAGE-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercise
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  2. Find the values of x for which f(x) = sqrt(sin x - cos x) is defined.

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  3. Draw the graph of y = tan^(2) x.

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  4. Draw the graph of y = sin x + cos x, x in [0, 2pi].

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  13. Draw the graph of f(x) = |tan x| + |cot x|.

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  14. Find the number of solutions to cos x = (x)/(10), x gt 0.

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  17. Solve :cos x le - (1)/(2).

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  18. Prove that the least positive value of x , satisfying tanx=x+1, lies i...

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  19. Draw the graph of y = (x^(2))/(10) sin x.

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  20. Draw the graph of y = (sin x)/(x).

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