Question

If (0°≤α≤90°) show that (sinα+ cosα) > 1

Answer 1

Answer:

sinα + cosα

=√(sinα+cosα)²

=√(sin²α+cos²α+2sinαcosα)

=√(1+sin2α)

if 0°≤α≤90° ───► 0°≤2α≤180°

►sin2α>0

►1+sin2α>1

►√(1+sin2α) > 1

so, (sinα+ cosα) > 1  if, (0°≤α≤90°)