Without using tables, give the value of each of the following :
`cos315^(@)`

Answer

To find the value of \( \cos 315^\circ \) without using tables, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Angle**:
We can express \( 315^\circ \) in terms of a known angle.
\[ 315^\circ = 360^\circ - 45^\circ \]

2. **Use the Cosine Identity**:
We can use the cosine identity for angles in the form \( \cos(360^\circ - \theta) \):
\[ \cos(360^\circ - \theta) = \cos \theta \]
Applying this identity:
\[ \cos 315^\circ = \cos(360^\circ - 45^\circ) = \cos 45^\circ \]

3. **Find the Value of \( \cos 45^\circ \)**:
We know from trigonometric values that:
\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]

4. **Conclusion**:
Therefore, substituting back, we find:
\[ \cos 315^\circ = \frac{1}{\sqrt{2}} \]

### Final Answer:
\[ \cos 315^\circ = \frac{1}{\sqrt{2}} \]

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