Home
Class 12
MATHS
Find the number of solution of the equat...

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

Text Solution

Verified by Experts

Put `e^(sin x)=t`
`rArr t^(2)-4t-1=0`
`rArr t=e^(sin x)=2 pm sqrt(5)`
Now `sin x in [-1, 1]`. Thus,
`e^(sin x) in [e^(-1), e^(1)]` and `2 pm sqrt(5) notin [e^(-1), e^(1)]`
Hence, there does not exist any solution.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

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

The solution of the equation e^(sinx) -e^(-sinx)-4 = 0 is :

Find the number of solution of the equation sinx=x^(2)+x+1 .

The number of solution of the equation e^(|x|)+|x|+e^(|x|)=4

Number of solutions of the equation 4x^(2)e^(-x)-1=0