Home
Class 12
MATHS
Draw the graph of y="cosec"("cosec"^(-1)...

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

Text Solution

Verified by Experts

`y=cosec(cosec^(-1)x)`
Clearly, the domain of the function is `(-oo,-1]cup[1,oo)`.
Now `cosec^(-1)x in[-pi/2,0)cup(0,pi/2]`
`:." cosec"("cosec"^(-1)x)in(-oo,-1]cup[1,oo)`
Also f(x) `="cosec"("cosec"^(-1)x)=x, " for "x in (-oo, -1]cup[1,oo)`
`y=sec(cec^(-1)x)`
Clearly, the domain of the function is `(-oo,-1]cup[1,oo)`
Now `sec^(-1)x in[0,pi/2)cup(pi/2,pi]`
`:." "sec(sec^(-1)x)in (-oo, -1]cup[-1,oo)`.
Also `f(x)=sec(sec^(-1)x)x," for "x in (-oo, -1]cup[1,oo).`
Thus, the graph of both the functions is the straight line y = x for `x in (-oo, -1]cup [1,oo)`.
Promotional Banner

Topper's Solved these Questions

  • GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|18 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise Exercises 1.18|1 Videos

  • GRAPHICAL TRANSFORMATIONS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION|78 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of y=sec^(-1)x+cosec^(-1)x

Draw in graph of y=" cosec"^(-1)("cosec x") .

Draw the graph of y=sec^(-1)|x| .

Draw the graph of y=cot^(-1)x+sec^(-1)x+cosec^(-1)x .

Draw the graph of f(x)=sec^(-1)(sec x)

Solve sec^(-1) x gt cosec^(-1) x

sec(cosec^-1x) is equal to

"cosec"sec^(-1)""((5)/(4))

Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? If yes, what is its fundamental period ?

Find the value of cos(sec^(-1)x+cosec^(-1)x),|x|ge1