If #tanhx=-7/25#, find the value of all the six hyperbolic functions of #x#?

Question

583 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-11T12:47:27

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

Some of the relations in hyperbolic functions are

#tanhx=sinhx/coshx#, #cosh^2x-sinh^2x=1#, #sech^2x=1-tanh^2x#

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

As #tanhx=-7/25# hence #cothx=-25/7#

#sech^2x=1-(-7/25)^2=1-49/625=576/625#

i.e. #sechx=24/25# and #coshx=25/24#

#sinhx=tanhx xx coshx=(-7/25)xx25/24=-7/24#

and #cschx=-24/7#