If sec theta cosh y = operatorname{cosec} x a | vedclass

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(A) Given equations are:$\sec 	heta \cosh y = \operatorname{cosec} x \implies \cos 	heta = \sin x \cosh y \quad (i)$$\operatorname{cosec} 	heta \si

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$\cos ^2 x$

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(A) Given equations are:$\sec 	heta \cosh y = \operatorname{cosec} x \implies \cos 	heta = \sin x \cosh y \quad (i)$$\operatorname{cosec} 	heta \sinh y = \sec x \implies \sin 	heta = \cos x \sinh y \quad (ii)$Squaring and adding equations $(i)$ and $(ii)$:$\cos ^2 	heta + \sin ^2 	heta = (\sin x \cosh y)^2 + (\cos x \sinh y)^2$$1 = \sin ^2 x \cosh ^2 y + \cos ^2 x \sinh ^2 y$Since $\cosh ^2 y = 1 + \sinh ^2 y$,we have:$1 = \sin ^2 x (1 + \sinh ^2 y) + \cos ^2 x \sinh ^2 y$$1 = \sin ^2 x + \sin ^2 x \sinh ^2 y + \cos ^2 x \sinh ^2 y$$1 = \sin ^2 x + \sinh ^2 y (\sin ^2 x + \cos ^2 x)$$1 = \sin ^2 x + \sinh ^2 y (1)$$\sinh ^2 y = 1 - \sin ^2 x$$\sinh ^2 y = \cos ^2 x$

If $\sec \theta \cosh y = \operatorname{cosec} x$ and $\operatorname{cosec} \theta \sinh y = \sec x$,then $\sinh ^2 y =$

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