Q.

The equation esin⁡x−e−sin⁡x=4 has:

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a

no real roots

b

exactly one real root

c

exactly four real roots

d

infinite number of real root

answer is A.

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Detailed Solution

Put esin⁡x=y. Note that 1/e≤y≤e.Also, the given equation can be written as            y−1/y=4 or y2−4y−1=0⇒       y=2±5.As 1/e≤y≤e, none of the two values of y is possible.
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The equation esin⁡x−e−sin⁡x=4 has: