Question:
If
\[
\cosech x=\frac45,
\]
then \(\sinh x=\)
If
\[ \cosech x=\frac45, \] then \(\sinh x=\)
\[ \cosech x=\frac45, \] then \(\sinh x=\)
Show Hint
Hyperbolic cosecant is simply the reciprocal of hyperbolic sine: \(\cosech x=\frac{1}{\sinh x}\).
Updated On: Jun 15, 2026
- \(\dfrac45\)
- \(\dfrac54\)
- \(\dfrac23\)
- \(\dfrac25\)
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The Correct Option is B
Solution and Explanation
Step 1: Recall the definition of \(\cosech x\).
We know that
\[ \cosech x=\frac{1}{\sinh x} \]
Given,
\[ \cosech x=\frac45 \]
Therefore,
\[ \frac{1}{\sinh x}=\frac45 \]
Step 2: Find \(\sinh x\).
Taking reciprocal on both sides,
\[ \sinh x=\frac54 \]
Step 3: Final conclusion.
Hence,
\[ \boxed{\frac54} \]
We know that
\[ \cosech x=\frac{1}{\sinh x} \]
Given,
\[ \cosech x=\frac45 \]
Therefore,
\[ \frac{1}{\sinh x}=\frac45 \]
Step 2: Find \(\sinh x\).
Taking reciprocal on both sides,
\[ \sinh x=\frac54 \]
Step 3: Final conclusion.
Hence,
\[ \boxed{\frac54} \]
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