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The sum of roots of the equation cos^(-1...

The sum of roots of the equation `cos^(-1)(cosx)=[x],[dot]` denotes the greatest integer function, is `2pi+3` (b) `pi+3` (c) `pi-3` (d) 2`pi-3`

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We have `cos^(-1)(cos x)=[x]`
To find the roods of the equation, we draw the graphs of `y=cos^(-1)(cos x)" and "y = [x]` and then find the points of intersection.

From the graph, roots are 0, 1, 2, 3, and the value ot x for which `3=2pi-x or x= 2 pi-3`. Hence the sum of roots is `2pi+3`
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CENGAGE PUBLICATION-GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS-Exercises
  1. The sum of roots of the equation cos^(-1)(cosx)=[x],[dot] denotes the ...

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  2. Draw the graph of y=tan^(-1)x-cot^(-1)x.

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  3. Find the number of real solutions to the equation 3cos^(-1)x-pix-pi/2=...

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  4. Evalute [lim(xto0) (sin^(-1)x)/(x)]=1, where[*] represets the greatest...

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  5. Solve tan^(-1)xgtcot^(-1)x graphically. Also find where f(x) = max. [t...

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  6. Match the colums.

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  7. Draw the graph of y=cos^(-1)sqrt(log([x])(|x|/x)) where [*] represents...

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  8. Find the value of int(0)^(100pi)sin^(-1)(sin x)dx.

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  9. Draw the graph of y=sin^(-1)((1)/(x))

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  10. Draw the graph of y=sin^(-1)(x^(2))

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  11. Draw the graph of y=cos^(-1)x^(3)" and compare with the graph of "y=co...

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  12. Draw the graph of y=cos^(-1)(2^(x)).

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  13. Draw the graph of y=cos^(-1){x}," where "{*}" represents the fractiona...

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  14. If cos^(-1)(cos x)=(n-x)/n,xge0, has seven roots, then find values of ...

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  15. Draw the graph of f(x)=[cot^(-1)x]," where "[*] represents the greate...

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  16. Draw the graph of y="cosec"("cosec"^(-1)x)" or "y=sec(sec^(-1)x).

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  17. Draw the graph of f(x) =cot^(-1)((2-|x|)/(2+|x|)).

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  18. Draw the graph of y=sin^(-1)(2xsqrt(1-x^(2)))

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  19. Draw the graph of y=(3x-x^(3))/(1-3x^(2)) and hence the graph of y=tan...

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