ABSTRACT
sinh x = e x − e − x 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq304.tif"/>
csch x = 1 sinh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq305.tif"/>
cosh x = e x + e − x 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq306.tif"/>
sech x = 1 cosh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq307.tif"/>
tanh x = e x − e − x e x + e − x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq308.tif"/>
ctnh x = 1 tanh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq309.tif"/>
sinh ( − x ) = − sinh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq310.tif"/>
ctnh ( − x ) = − ctnh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq311.tif"/>
cosh ( − x ) = cosh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq312.tif"/>
sech( − x ) = s ech x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq313.tif"/>
tanh ( − x ) = − tanh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq314.tif"/>
c sch ( − x ) = − csch x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq315.tif"/>
tanh x = sin x cosh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq316.tif"/>
ctnh x = cosh x sinh x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq317.tif"/>
cosh 2 x − sinh 2 x = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq318.tif"/>
cosh 2 x = 1 2 ( cosh 2 x + 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq319.tif"/>
sinh 2 x = 1 2 ( cosh 2 x − 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq320.tif"/>
ctnh 2 x -csch 2 x = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq321.tif"/>
csch 2 x − sech 2 x = csch 2 x sech 2 x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq322.tif"/>
tanh 2 x + sech 2 x = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq323.tif"/>
sinh ( x + y ) = sinh x cosh y + cosh x sinh y cosh ( x + y ) = cosh x cosh y + sinh x sinh y sinh ( x − y ) = sinh x cosh y − cosh x sinh y cosh ( x − y ) = cosh x cosh y − cosh x sinh y https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq324.tif"/> tanh ( x + y ) = tanh x + tanh y 1 + tanh x tanh y tanh ( x − y ) = tanh x − tanh y 1 − tanh x tanh y https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203743102/9cca8f32-4688-4a1e-80c2-a6c9068f5153/content/eq325.tif"/>