If operatorname{Sinh}^{-1}(2)+operatorname{Si | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha$. Let $x = \operatorname{Sinh}^{-1}(2)$ and $y = \operatorname{Sinh}^{-1}(3)

Vedclass · Accepted Answer

$2 \sqrt{10}+3 \sqrt{5}$

Vedclass · Answer

(D) Given $\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha$. Let $x = \operatorname{Sinh}^{-1}(2)$ and $y = \operatorname{Sinh}^{-1}(3)$. Then $\sinh x = 2$ and $\sinh y = 3$. We know that $\cosh^2 x - \sinh^2 x = 1$,so $\cosh x = \sqrt{1 + \sinh^2 x} = \sqrt{1 + 2^2} = \sqrt{5}$. Similarly,$\cosh y = \sqrt{1 + \sinh^2 y} = \sqrt{1 + 3^2} = \sqrt{10}$. We need to find $\sinh \alpha = \sinh(x+y)$. Using the identity $\sinh(x+y) = \sinh x \cosh y + \cosh x \sinh y$: $\sinh \alpha = (2)(\sqrt{10}) + (\sqrt{5})(3) = 2 \sqrt{10} + 3 \sqrt{5}$.

If $\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha$,then $\sinh \alpha=$

Similar Questions

If $\sinh x = -\frac{4}{3}$,then $\sinh 2x + \cosh 2x = $

If $\tan A + \cot A = 4$,then $\tan^4 A + \cot^4 A$ is equal to

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

If the roots of $x^3 + ax^2 + bx + c = 0$ are the cosines of the angles of an acute triangle,then the value of $a^2 - 2b - 2c$ is:

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$,then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module