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Question

Assertion :The function sinh(x) is an odd function. Reason: The function sinh(x) is symmetric with respect to the origin, and sinh(0)=0.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Assertion
. sinhx is an odd function
f(x)=sinhx=exex2
f(x)=sinh(x)=exe(x)2=(exex)2=f(x)
f(x)=f(x) , which shows f(x) is an odd function.
Reason
Yes sinhx is symmetrical w.r.t. 0
And it is also the condition to be an odd function.
And odd function is symmetric at origin.
coshex is even function
f(x)=coshx=ex+ex2
f(x)=cosh(x)=ex+e(x)2=(ex+ex)2=f(x)
Hence function is even function.
The graph of coshx s which is symmetric about y axis.
And the condition of even function is f(x)=f(x)
and symmetric about y axis
Hence Assertion and Reason both are correct and Reason is correct explanation of Assertion.

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