Home
Class 12
MATHS
the equation e^(sinx)-e^(-sinx)-4=0 has....

the equation `e^(sinx)-e^(-sinx)-4=0` has.

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.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise JEE ADVANCED|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise Numerical Value Type|20 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE ENGLISH|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

The equation e^(sin x)-e^(-sin x)-4=0 has

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

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) , is

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

Between any two real roots of the equation e^(x)sinx-1=0 the equation e^(x)cosx+1=0 has

If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi] are real, then the values of b are [-2,0] (b) (-2,0) [-2,0] (d) non eoft h e s e

If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi] are real, then the values of b are [-2,0] (b) (-2,0) [-2,0] (d) non eoft h e s e

The number of distinct real roots of the equation |{:(cosx, sinx, sinx), (sinx, cosx, sinx), (sinx, sinx, cosx):}|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

The number of solutions of the equation e^(|sinx|)=sec x for all x in (-pi//2,pi//2) is/are

Integrate the functions e^(2x)sinx

CENGAGE ENGLISH-LOGARITHM AND ITS PROPERTIES-JEE MAIN
  1. the equation e^(sinx)-e^(-sinx)-4=0 has.

    Text Solution

    |