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The value of sinh(3) cosh(3) =
A. e3
B. e3
C. e3
D. e3

Answer
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Hint: Now, in this question hyperbolic trigonometric functions of cos and sin are mentioned. The hyperbolic functions are to be written in the exponential functions. Thereafter we will have to simplify the obtained equation to find the trigonometric equation’s value.
Formula used: We will have to use the formula of hyperbolic cos function, coshx =ex+ex2 and hyperbolic sine function, sinhx =exex2 .

Complete step-by-step answer:
According to the given information, we have
The first function is A= sinh(3)
The formula for sinhx in terms of exponential function is,
 sinhx =exex2
Substituting x=3 in the above given equation we get,
 sinh(3) =e3e32 ...(1)
The first function is B= cosh(3)
The formula for coshx in terms of exponential function is,
 coshx =ex+ex2
Substituting x=3 in the above given equation we get,
 cosh(3) =e3+e32 ...(2)
According to the given data we have to calculate sinh(3) cosh(3) , which is equal to,
 sinh(3) cosh(3) =e3e32 e3+e32
e3e3(e3e3)2
2e32=e3
So, the correct answer is “Option B”.

Note: In order to solve problems of this type the key is to have a basic understanding of trigonometric equations and values and also learn its implications. Hyperbolic functions are very similar to the trigonometric functions but are expressed in the form of exponential functions and the most common of them are coshx and sinhx .
The formula for coshx in terms of exponential function is,
 coshx =ex+ex2
The formula for sinhx in terms of exponential function is,
 sinhx =exex2
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