sin^4π/8 +cos^4π/8

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sin^4π/8 +cos^4π/8

sin^4π/8 +cos^4π/8
sin^4π/8 +cos^4π/8

sin^4π/8 +cos^4π/8
sin^4π/8+cos^4π/8
=(sin²π/8+cos²π/8)²-2sin²π/8cos²π/8
=1-2(sinπ/8cosπ/8)²
而 sinπ/8cosπ/8=1/2sinπ/4=√2/4
所以原式 =1-2(√2/4)²
=3/4.

sin^4(π/8) +cos^4(π/8)
=[sin^4(π/8) +cos^4(π/8)+2sin²(π/8)cos²(π/8)]-2sin²(π/8)cos²(π/8)
=[sin²(π/8) +cos²(π/8)]²-[2sin(π/8)cos(π/8)]²/2
=1-[sin²(π/4)]/2
=1-1/4
=3/4

sin⁴(π/8) +cos⁴(π/8 )=[sin²(π/8)+cos²(π/8)]²-2sin²(π/8)cos²(π/8)
=1-(1/2)sin²(π/4)=1-(1/2)(√2/2)²=1-1/4=3/4