Question

if tanh(x)=1/3 then tanh(3x) is​

Answer 1

Given : tanh(x)=1/3

To Find :  tanh (3x)

Solution:

tanh(x)=1/3

tanh(x)=   (eˣ - e⁻ˣ )/ (eˣ + e⁻ˣ )

tanh(3x)=   (e³ˣ - e⁻³ˣ )/ (e³ˣ + e⁻³ˣ )

(eˣ - e⁻ˣ )/ (eˣ + e⁻ˣ )  = 1/3

=> 3eˣ - 3e⁻ˣ = eˣ + e⁻ˣ

=> 2eˣ = 4e⁻ˣ

=> eˣ = 2e⁻ˣ

=>  e³ˣ = 8e⁻³ˣ

tanh(3x)=   (e³ˣ - e⁻³ˣ )/ (e³ˣ + e⁻³ˣ )

=    (8e⁻³ˣ - e⁻³ˣ )/ (8e⁻³ˣ + e⁻³ˣ )

= 7e⁻³ˣ  / 9e⁻³ˣ

=  7/9

tanh (3x) = 7/9

or other method :

tanh(3x)=  (3tanhx+tanh³x) /( 1+3tanh²x)  

Substitute tanhx = 1/3

= (3(1/3) + (1/3)³) / ( 1 + 3(1/3)²)

= ( 1 + 1/27)/ ( 1 + 1/3)

= (28/27) /( 4/3)

= 7/9

tanh (3x) = 7/9

Learn More:

Show that sinix=isinhx​

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