cos平方乘以π/8-sin平方乘以π/8详细过程

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cos平方乘以π/8-sin平方乘以π/8详细过程
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cos平方乘以π/8-sin平方乘以π/8详细过程
cos平方乘以π/8-sin平方乘以π/8
详细过程

cos平方乘以π/8-sin平方乘以π/8详细过程
因为{[sin(π/8)]^2}+{[cos(π/8)]^2}=1
所以:[cos(π/8)]^2=1-[sin(π/8)]^2
所以:{[cos(π/8)]^2}-{[sin(π/8)]^2}=1-2[sin(π/8)]^2
因为:π/8=45°/2
所以:如图,可求得sin(45°/2)=[(√2)-1]/√(4-2√2)
所以:2[sin(π/8)]^2=2[sin(45°/2)]^2=(3-2√2)/(2-√2)
所以:{[cos(π/8)]^2}-{[sin(π/8)]^2}=1-(3-2√2)/(2-√2)
即:{[cos(π/8)]^2}-{[sin(π/8)]^2}=[(√2)-1]/(2-√2)