Without using calculator, prove that :
sin 30 sin 10/sin 50 = tan 30 tan 10/(1 - tan 30 tan 10). All in degrees.
Trigonometry
2015-04-11 7:06 pm
回答 (1)
2015-04-11 7:46 pm
✔ 最佳答案
prove:sin 30 sin 10/sin 50=tan 30 tan 10/(1-tan 30 tan 10)
right
=tan 30 tan 10/(1- tan 30 tan 10)
=(cos 30 cos 10)(sin 30/cos 30)(sin 10/cos 10)/ [(cos 30 cos 10)(1-(sin 30/cos 30)(sin 10/cos 10)]
=(sin 30)(sin 10)/(cos 30 cos 10-sin 30 sin 10)
=sin 30 sin 10/cos(30+10)
=sin 30 sin 10/cos 40
=sin 30 sin 10/sin 50
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