If sin α + sin β = cos α + cos β = 1, then sin α + cos α = ?
Explanation:
sin α + sin β = 1
sin² α + sin² β + 2 sin α sin β = 1 ...(1)
cos α + cos β = 1
cos² α + cos² β + 2 cos α cos β = 1 ...(2)
Adding (1) and (2),
(sin² α + cos² α) + (sin² β + cos² β) + 2 sin α sin β + 2 cos α cos β = 1 + 1
1 + 1 + 2 sin α sin β + 2 cos α cos β = 2
2 [cos α cos β + sin α sin β] = 0
cos (β - α) = 0
β - α = 90°
β = 90° + α
sin α + sin (90° - α) = 1
sin α + cos α = 1
Hence, the correct answer is Option C