已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.

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已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.a属于(

已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.
已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.

已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.
a属于(0,派)且cos(a-派/6)=3/5
所以
sin(a-派/6)=4/5
从而
cosa=cos(a-π/6+π/6)
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
=3/5×√3/2-4/5×1/2
=(3√3-4)/10

0-Pai/6故有sin(a-Pai/6)=(+/-)4/5
cosa=cos(a-Pai/6+Pai/6)
=cos(a-Pai/6)cosPai/6-sin(a-Pai/6)sinPai/6
=3/5*根号3/2-(+/-)4/5*1/2
=(3根号3(-/+)4)/10

∵1/2<3/5<√2/2
∴π/4即5π/12又∵a属于(0,π)
∴5π/12即π/4∴sin(a-π/6)=√[1-cos²(a-π/6)]=4/5
cosa=cos[(a-π/6)+π/6]

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∵1/2<3/5<√2/2
∴π/4即5π/12又∵a属于(0,π)
∴5π/12即π/4∴sin(a-π/6)=√[1-cos²(a-π/6)]=4/5
cosa=cos[(a-π/6)+π/6]
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
=3/5*(√3/2)-4/5*(1/2)
=(3√3-4)/10

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