Trigonometrical Equations Ques 1

  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

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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.



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