If #tanh x =7/25# how do you find the values of the other hyperbolic functions at x?

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Answer 1 · 2016-12-25T17:08:07

#sinhx=7/24#, #coshx=25/24#, #tanhx=7/25#
#cothx=25/7#, #sechx=24/25#, #cschx=24/7#

Apart from the usual relations that

#tanhx=sinhx/coshx#, #cothx=coshx/sinhx#, #sechx=1/coshx# and #cschx=1/sinhx#,

some other relations we can use are

#cosh^2x-sinh^2x=1# and #tanh^2x+sech^2x=1#

Hence, as #tanhx=7/25#, #cothx=25/7#

#sechx=sqrt(1-7^2/25^2)=sqrt(1-49/625)=sqrt(576/625)=24/25#

#coshx=25/24#, #sinhx=tanhx xx coshx=7/25xx25/24=7/24# and

#cschx=24/7#