Question

Assertion :The graph of the function $f\left(x\right)=\sinh \left(x\right)+\cosh \left(x\right)$ is exponential. Reason: The function $f\left(x\right)=\sinh \left(x\right)+\cosh \left(x\right)$ can be realised as an exponential function by substituting $\sinh \left(x\right)=\frac{e^x-e^{-x}}{2}$ and $\cosh \left(x\right)=\frac{e^x+e^{-x}}{2}$

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

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$f\left(x\right)=\sinh x+\cosh x$

$=\frac{e^x-e^{-x}}{2}+\frac{e^x+e^{-x}}{2}$

$=\frac{e^x-e^{-x}+e^x+e^{-x}}{2}$

$=\frac{2e^x}{2}=e^x$ exponential function

Reason: It is given that $\sinh x=\frac{e^x-e^{-x}}{2}$ and, $\cosh x=\frac{e^x+e^{-x}}{2}$

Hence assertion and reason are correct and reason is the correct explanation of assertion.