已知a为锐角sina-cosa=7/5 a∈(0,π)(1)tana(2)sina+cosa(3)sin^3a+cos^3a
问题描述:
已知a为锐角sina-cosa=7/5 a∈(0,π)
(1)tana
(2)sina+cosa
(3)sin^3a+cos^3a
答
∵a∈(0,π)则
{sina-cosa=7/5 ①
{sin²a+cos²a=1 ②
{sina>0
①==>cosa=sina-7/5代入②
sin²a+(sina-7/5)²=1
∴sin²a-7/5sina+12/25=0
解得:
sina=4/5,(舍负)
cosa=-3/5
∴tana=sina/cosa=-4/3
(2)
∴sina+cosa=1/5
(3)
sin^3a+cos^3a
=(4/5)³+(-3/5)³
=64/125-27/125
=37/125