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01.07.2019 •
Mathematics
If tanh x = 12 13 , find the values of the other hyperbolic functions at x. sinh x = 12/5 correct: your answer is correct. cosh x = 13/5 correct: your answer is correct. coth x = 13/12 correct: your answer is correct. sech x = 5/13 correct: your answer is correct. csch x = 5/12 correct: your answer is correct.
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Ответ:
1) Calculate cosh x:
cosh² x = 1/(1-tanh² x) →→ 1/[1-(12/13)²] = 1/(1-144/169) = 1/[(169-144)169]
cosh²x = 169/25 and cosh x = + or - 13/5
2) Calculate sinh x
sinh x/cosh x = tanh x →→sinh x = (cosh x)(tanh x)
sinh x = + or - (13/5)(12/13) →→sinh x= + or - 12/5
From here onward you can calculate easily coth x, sech x, csch x
Ответ: