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19 changes: 19 additions & 0 deletions content/pytorch/concepts/tensors/terms/cosh/cosh.md
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# .cosh()

## Introduction
The `.cosh()` function in PyTorch computes the **hyperbolic cosine** of each element in the input tensor. The hyperbolic cosine, denoted as `cosh(x)`, is a mathematical function that is useful in various fields, including geometry, physics, and machine learning.

The hyperbolic cosine is defined as:
\[
\cosh(x) = \frac{e^x + e^{-x}}{2}
\]

In PyTorch, the `.cosh()` function allows you to apply this operation **element-wise** to all elements of a tensor, which is particularly useful for tensor computations in scientific and engineering applications.

---

## Syntax
```python
torch.cosh(input, *, out=None) -> Tensor