1、1/(3-2cos²22.5°)=1/[3-(1+cos45°)]=1/(2-√2/2)=(4+√2)/7;
2、cos²10°/(1+cos20°)=2cos²10°/(2+2cos20°)=(1+cos20°)/(2+2cos20°)=1/2;
3、(√2+1)tan²(π/8)=(√2+1)sin²(π/8)/cos²(π/8)=(√2+1)[1-cos²(π/8)]/cos²(π/8)]
=(√2+1)[1/cos²(π/8)-1]=(√2+1){2/[1+cos(π/4)]-1}
=(√2+1)(3-2√2)=√2-1
希望能帮到你!