3／cos²20°－1/sin²20°＋64sin²20°

3／cos²20°－1/sin²20°＋64sin²20°
3／cos²20°－1/sin²20°＋64sin²20°

3／cos²20°－1/sin²20°＋64sin²20°
3/sin20^2-1/cos20^2+64sin20^2
=[3(cos20)^2-(sin20)^2]/(sin20)^2(cos20)^2+64(sin20)^2
=[(√3cos20+sin20)(√3cos20-sin20)]/(sin20cos20)^2+64(sin20)^2
=[2sin(60+20)*2sin(60-20)]/[(sin40)/2]^2+64(sin20)^2
=16sin80sin40/sin40*sin40+64(sin20)^2
=16sin80/sin40+64(sin20)^2
=32sin40cos40/sin40+64(sin20)^2
=32cos40+64(sin20)^2
=32[1-2(sin20)^2]+64(sin20)^2
=32