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05.08.2020 10:00
Алгебра
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Косинус(п + 2x) дорівнює одиниці​

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vladt12092002
vladt12092002
4,8(61 оценок)
1)sin20⁰cos10⁰+cos20⁰sin10⁰= =1/2[sin(20⁰+10⁰)+sin(20⁰-10⁰)]+1/2[sin(10⁰+20⁰)+sin(10⁰-20⁰)]= =1/2[sin30⁰+sin10⁰]+1/2[sin30⁰+sin(-10⁰)]=sin30⁰+1/2sin10⁰-1/2sin10⁰= =sin30⁰=1/2; 2)sinπ/5cos4π/5+cosπ/5sin4π/5= =1/2[sin(π/5+4π/5)+sin(π/5-4π/5)]+1/2[sin(4π/5+π/5)+sin(4π/5-π/5)]= =1/2[sinπ+sin(-3π/5)]+1/2[sinπ+sin(3π/5]= =sinπ-1/2sin(3π/5)+1/2sin(3π/5)= =sinπ=0; 3)cos80⁰cos10⁰+sin80⁰cos10⁰= =1/2[cos(80⁰-10⁰)+cos(80⁰+10)⁰]+1/2[sin(80⁰+10⁰)+sin(80⁰-10⁰)]= =1/2[cos70⁰+cos90⁰]+1/2[sin90⁰+sin70⁰]= =1/2[cos70⁰+0]+1/2[1+sin70⁰]=1/2cos70⁰+1/2sin70⁰+1/2; 4)cos3π/8sinπ/8+cosπ/8sin3π/8= =1/2[sin(π/8+3π/8)+sin(π/8-3π/8)]+1/2[sin(3π/8+π/8)+sin(3π/8-π/8)]= =1/2[sin(π/2)+sin(-π/4)]+1/2[sin(π/2)+sin(π/4)]= =sin(π/2)-1/2sin(π/4)+1/2sin(π/4)=sin(π/2)=1;

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