tan67°30′-tan22°30′=?过程tan67°30′-tan22°30′=
问题描述:
tan67°30′-tan22°30′=?
过程tan67°30′-tan22°30′=
答
tan67°30′-tan22°30′=?//: 利用下式:tan a-tan b=2sin(a-b)/[cos(a+b)+cos(a-b)];
tan67°30′-tan22°30′
=2sin(67.5°-22.5°)/[cos(67.5°+22.5°)+cos(67.5°-22.5°)]
=2 sin 45° / cos 45°
=2 tan 45°
=2
答
化成正、余弦来求解原式=tan67°30′-cot67°30′=sin67°30′/cos67°30′-cos67°30′/sin67°30′=(sin67°30′^2-cos67°30′^2)/(sin67°30′*cos67°30′)=2(1-2cos67°30′^2)/sin135°=2*(-cos135...