Wiedząc, że liczba sin α + cos α = √5/2 oblicz liczbę b= (sin α - cos α)²
sin α + cos α = √5/2/², podnoszę obustronnie do potęgi 2
sin²+2sinacosa+cos²a=5/4, poniewaz sin^2+cos^2=1
1+2sinacosa=5/4
2sinacosa=5/4-1=1/4
b= (sin α - coas α)²=sin²a-2sinacosa+cos²a=1-1/4=3/4
więc
b=1-3/2=-1/2
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sin α + cos α = √5/2/², podnoszę obustronnie do potęgi 2
sin²+2sinacosa+cos²a=5/4, poniewaz sin^2+cos^2=1
1+2sinacosa=5/4
2sinacosa=5/4-1=1/4
b= (sin α - coas α)²=sin²a-2sinacosa+cos²a=1-1/4=3/4
więc
b=1-3/2=-1/2