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Observe the following statements: Asse...

Observe the following statements:
Assertion(A) : If `-(pi)/(2) lt theta lt (pi)/(2) and x=log_(e ) ((1+sin theta)/(cos theta))` then `sinhx=tan theta`
Reason (R ) : For `-(pi)/(2) lt theta lt (pi)/(2)`, the value of `sec theta` is positive.
Then the true statement among the following is

A

A is false, R is false

B

A is false, R is ture

C

A is true, R is false

D

A is true, R is true, `R rArr A`

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The correct Answer is:
D
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AAKASH SERIES-HYPERBOLIC FUNCTIONS -EXERCISE - II
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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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