sin 75° + cos 75°

sin 75° = sin (45° + 30°)
= sin 45°cos 30° + cos 45°sin 30°
= (√2/2 √3/2) + (√2/2 1/2)
= (√6 + √2) / 2

cos 75° = cos (45° + 30°)
= cos 45°cos 30° - sin 45°sin 30°
= (√2/2 √3/2) - (√2/2 1/2)
= (√6 - √2) / 2

Therefore, sin 75° + cos 75° = ((√6 + √2) / 2) + ((√6 - √2) / 2)
= √6/2 + √2/2
= (√6 + √2) / 2

So, sin 75° + cos 75° = (√6 + √2) / 2