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.