sin(67`1/2)^(@) + cos(`67`1/2)^(@)` is equal to A) `1/2sqrt(4+2sqrt(2))`, B) `1/2sqrt(4-2sqrt(2))`, C) `1/4(sqrt(4+2sqrt(2)))`, D) `1/4(sqrt(4-2sqrt(2)))`

Explanation

To solve the problem \( \sin(67.5^\circ) + \cos(67.5^\circ) \), we can use the identity for the sum of sine and cosine:

### Step 1: Use the identity
We know that:
\[ \sin a + \cos a = \sqrt{1 + \sin(2a)} \]
Here, \( a = 67.5^\circ \).
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