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Find Tanhx If 5sinhx-coshx = 5 - Applied Mathematics 1

Find tanhx if 5sinhx-coshx = 5 

 

 

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Solution

`5sinhx-coshx=5`

But  sinhx=`(e^x-e^-x)/z`    coshx= `(e_x+e^-x)/2` 

∴ 5`[(e_x-e_r)/z]-[(e^x+e^-x)/2]=5`

∴ `5e^x-5e^-x-e^x-e^-x=10`

∴ `4e^(2x)-10e^x-6=0`

Roots are : `e^x=3,e^x=-1/2` 

∴ tanhx=`(e^x-e^-x)/(e^x+e^-x)=((1/2)+2)/(-5/2)=(-3)/5`

or 

∴ tanhx=`(e^x-e^-x)/(e^x+e^-x)=(3-1/3)/(3+1/3)=4/5` 

The values of tanhx are : `(-3)/5  or  4/5`

 

Concept: Separation of Real and Imaginary Parts of Logarithmic Functions
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