If sinh x = frac{3}{4} and cosh y = frac{5}{3 | vedclass

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

Question

(B) Given $\sinh x = \frac{3}{4}$.Using the formula $\sinh^{-1} z = \log(z + \sqrt{z^2 + 1})$:$x = \log(\frac{3}{4} + \sqrt{(\frac{3}{4})^2 + 1}) = \l

Vedclass · Accepted Answer

$\log 6$

Vedclass · Answer

(B) Given $\sinh x = \frac{3}{4}$.Using the formula $\sinh^{-1} z = \log(z + \sqrt{z^2 + 1})$:$x = \log(\frac{3}{4} + \sqrt{(\frac{3}{4})^2 + 1}) = \log(\frac{3}{4} + \sqrt{\frac{9}{16} + 1}) = \log(\frac{3}{4} + \frac{5}{4}) = \log(2)$.Given $\cosh y = \frac{5}{3}$.Using the formula $\cosh^{-1} z = \log(z + \sqrt{z^2 - 1})$:$y = \log(\frac{5}{3} + \sqrt{(\frac{5}{3})^2 - 1}) = \log(\frac{5}{3} + \sqrt{\frac{25}{9} - 1}) = \log(\frac{5}{3} + \frac{4}{3}) = \log(3)$.Therefore,$x + y = \log 2 + \log 3 = \log(2 	imes 3) = \log 6$.

If $\sinh x = \frac{3}{4}$ and $\cosh y = \frac{5}{3}$,then $x + y =$

Similar Questions

If $\sqrt{a + ib} = x + iy$,then the possible value of $\sqrt{a - ib}$ is

If $\theta = \frac{\pi}{12}$ and $x = \log \left(\cot \left(\frac{\pi}{4} + \theta\right)\right)$,then $\cosh x =$

If $\tanh^{-1}(x+iy) = \frac{1}{2} \tanh^{-1}\left(\frac{2x}{1+x^2+y^2}\right) + \frac{i}{2} \tan^{-1}\left(\frac{2y}{1-x^2-y^2}\right)$,where $x, y \in \mathbb{R}$,then $\tanh^{-1}(iy) =$

$\sinh^{-1}\left(2^{3/2}\right)$ is equal to :

If $(-7 - 24i)^{1/2} = x - iy$,then $x^2 + y^2 = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module