Trigonometrical Equations Ques 1
- The number of solutions of the equation $\sin \left(e^x\right)=5^x+5^{-x}$ is
(1991, 2M)
(a) $0$
(b) $1$
(c) $2$
(d) infinitely many
Show Answer
Answer:
Correct Answer: 1.(a)
Solution: (a) Given equation is $\sin \left(e^x\right)=5^x+5^{-x}$ is
LHS $ =\sin \left(e^x\right)<1, \forall x \in R $
and RHS $ =5^x+5^{-x} \geq 2 $
$\therefore \quad \sin \left(e^x\right) =5^x+5^{-x} $ has no solution.
BETA
