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Statement-I: If f(x) = coshx - sinhx for...

Statement-I: If f(x) = coshx - sinhx for `x in R` then `f(x-y)=f(x) div f(y)`
Statement -II: If f(x) = coshx + sinhx for `x in R` then f(x) is a bijective function
Statement-III: `coth^(-1)x="cosh"^(-1)(|x|)/(sqrt(x^(2)-1))`
Which of the above statement is correct?

A

only I, II

B

only II, III

C

only I and III

D

I, II, III

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-HYPERBOLIC FUNCTIONS -EXERCISE - II
  1. sin h^(-1) ((x)/(sqrt(1 - x^(2)))) =

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  2. The point of intersection of the curves y=cosh(x) and y=sech(x) is

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  3. The domain of cos h^(-1) (2x) is

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  4. If 'x' is an acute angle and y=log(tan((pi)/(4)+(x)/(2))) then cosx.co...

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  5. Statement-I: If f(x) = coshx - sinhx for x in R then f(x-y)=f(x) div ...

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  6. Statement-I: If sechx + cosechx ="k"(e^((k-1)x))/(e^(kx)-1) then k = 3...

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  7. Arrange the following in ascending order of their values (A) cosh2 ...

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  8. If 2(sinh2+sinh3+sinh5) (e^(5))/(e^(5)-1)=a+be^(2)+ce^(3)+de^(5) then ...

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  9. Match from List-I to List-II {:("List-I","List-II"),("(Function)","(...

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  10. Observe the following statements: Assertion(A) : If -(pi)/(2) lt the...

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  11. Observe the following statements: Assertion (A): If "sinh"^(-1) sqrt...

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  12. If tanA=tan alpha tanh beta and tanB=cot alpha tan h beta then tan(A+...

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  13. log[(x-1)+sqrt(x^(2)-2x)], x ge 2, is equal to

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  14. For 0 lt x le pi, sinh^(-1) (cotx)=

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  15. tan h^(-1) ((1)/(2)) + cot h^(-1) (2) =

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  16. The domain of sech^(-1)((x)/(2)) is

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  17. If x=tanh^(-1)(y), then log(e )((1+y)/(1-y))=

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  18. sec h^(-1) ((1)/(2)) - "cosec h"^(-1) ((3)/(4)) =

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  19. If 2"sinh"^(-1)((a)/(sqrt(1-a^(2))))=log((1+x)/(1-x)) then x =

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  20. If cos h (x)=(5)/(4), then cos h (3x)=

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