Get Answers to all your Questions

header-bg qa

The equation e^{\sin x}-e^{-\sin x}-4=0 has

  • Option 1)

    infinite number of real roots

  • Option 2)

    no real roots

  • Option 3)

    exactly one real root

  • Option 4)

    exactly four real roots

 

Answers (2)

best_answer

e^{\sin x}-e^{-\sin x}-4= 0

\left ( e^{\sin x} \right )^{2}-4e^{\sin x}-1= 0\Rightarrow t^{2}-4t-1= 0

\Rightarrow t= \frac{4\pm \sqrt{16+4}}{2}= 2\pm \sqrt{5}

i.e.,e^{\sin x}= 2+\sqrt{5}\: or  

\sin x= ln\left ( 2+\sqrt{5} \right )> 1\therefore No \, real \, root


Option 1)

infinite number of real roots

Option 2)

no real roots

Option 3)

exactly one real root

Option 4)

exactly four real roots

Posted by

solutionqc

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE