一道自招数学三角函数题如图
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一道自招数学三角函数题如图一道自招数学三角函数题如图一道自招数学三角函数题如图cosπ/13*cos4π/13+cos3π/13*cos4π/13-cosπ/13*cos3π/13=1/2*[cos3
一道自招数学三角函数题如图
一道自招数学三角函数题
如图
一道自招数学三角函数题如图
cosπ/13 *cos4π/13 +cos3π/13 *cos4π/13-cosπ/13 *cos3π/13
=1/2*[cos3π/13+cos5π/13+cosπ/13+cos7π/13-cos2π/13-cos4π/13]
注意到cos2π/13=-cos11π/13,cos4π/13=-cos9π/13
原式=1/2*[cosπ/13+cos3π/13+cos5π/13+cos7π/13+cos9π/13+cos11π/13]
=1/2*[sinπ/13*cosπ/13+sinπ/13*cos3π/13+sinπ/13*cos5π/13+sinπ/13*cos7π/13+sinπ/13*cos9π/13+sinπ/13*cos11π/13]/(sinπ/13)
=1/4*(sin2π/13+sin4π/13-sin2π/13+sin6π/13-sin4π/13+sin8π/13-sin6π/13+sin10π/13-sin8π/13+sin12π/13-sin10π/13)/(sinπ/13)
=1/4*(sin12π/13)/(sinπ/13)
=1/4