(B) We know the fundamental identity for hyperbolic functions: $\cosh^2 u - \sinh^2 u = 1$. Given that $\sinh u = \tan \theta$. Substituting this into

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(B) We know the fundamental identity for hyperbolic functions: $\cosh^2 u - \sinh^2 u = 1$. Given that $\sinh u = \tan \theta$. Substituting this into the identity,we get: $\cosh^2 u - (\tan \theta)^2 = 1$. $\cosh^2 u = 1 + \tan^2 \theta$. Using the trigonometric identity $1 + \tan^2 \theta = \sec^2 \theta$,we have: $\cosh^2 u = \sec^2 \theta$. Therefore,$\cosh u = \sec \theta$ (since $\cosh u$ is always positive).

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $\sinh u = \tan \theta$,then $\cosh u$ is equal to

AP EAMCET 2021 All AP EAMCET

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$-\sec \theta$
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$\sec \theta$
C
$\sin \theta$
D
$\cot \theta$

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Trigonometrical Ratios, Functions and Identities

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Mix Examples-Trigonometrical Ratios, Functions and Identities

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