tan7.5-tan7.求值 要给出方法跟过程啊.

tan7.5-tan7.求值 要给出方法跟过程啊.
tan7.5-tan7.求值 要给出方法跟过程啊.

tan7.5-tan7.求值 要给出方法跟过程啊.
是 tan 7.5° -1/ tan 7.5° 吗?
= = = = = = = = =
tan 7.5° -1/ tan 7.5°
=sin 7.5° /cos 7.5° -cos 7.5° /sin 7.5°
= [ (sin 7.5°)^2 -(cos 7.5°)^2 ] / (sin 7.5° cos 7.5°)
= -cos 15° / [ (1/2) sin 15° ]
= -2 cot 15°.
= -2 tan 75°.
又因为 tan 75°=tan (45° +30°)
= (tan 45° +tan 30°) / (1 -tan 45° tan 30°)
= [ 1 +(根号3) /3 ] / [ 1- (根号3) /3 ]
= 2 +根号3,
所以 tan 7.5° -1/ tan 7.5° = -4 -2根号3.
= = = = = = = = =
15°,75°是特殊角.
已用计算器验证.