Home
Class 12
MATHS
Show that the equation e^(sinx)-e^(-sinx...

Show that the equation `e^(sinx)-e^(-sinx)-4=0` has no real solution.

A

infinite number of real roots

B

no real roots

C

exactly one real root

D

exactly four real roots

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` e^(sin x) = t`
` rArr t^(2) - 4t - 1= 0`
` rArr t = (4 pm sqrt(16+4))/2`
` rArr t=e^(sin x) = 2 pm sqrt5`
` rArr e^(sin x) = 2 - sqrt5, e^(sin x ) = 2 + sqrt 5 `
` e ^(sin x ) = 2 - sqrt 5 lt 0 ` ,
` rArr sin x = "In " (2+sqrt5) gt 1`
So it is rejected, hence there is no solution.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Numerical)|18 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has at least one solution in the interval (0,pi/2) (a) 9 (b) 4 (c) 8 (d) 1

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

Integrate the functions e^(x)sinx

For what value of k the equation sinx+cos(k+x)+cos(k-x)=2 has real solutions?

Integrate the functions e^(2x)sinx

Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(sinx))=cos("sin"(cosx)) has only one solution in [0,pi/2]dot

Find the number of solution of the equation e^(sinx)-e^(-sinx)-4=0

Integrate the functions e^(x)(sinx+cosx)dx

Minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solution,

Number of integral value(s) of m for which the equation sinx-sqrt(3)cosx=(4m-6)/(4-m) has solutions, x in [0,2pi] , is ________

Home
Profile