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