1证明sin^2a/1+cota + cos^2a/1+tana =1-sinacosa
2求证(2-cos^2a)(1+2cot^2a)=(2+cot^2a)(2-sin^2a)
3已知tana=-1/2求下列式子等于多少
1 sin^2a-2sinacosa-cos^2a/4cos^a-3sin^2a+1
2 sin^2a-3sinacosa-1
3 1/4sin^2a+2/5cos^2a
前2个证明详细点.最后一个告诉下思路和结果就可以了.谢谢了哈
參考答案:1证明sin^2a/1+cota + cos^2a/1+tana =1-sinacosa
左边=sin^3a/(sina+cosa)+cos^3a/(sina+cosa)
=(sin^3a+cos^3a)/(sina+cosa)
=sin^2a-sinacosa+cos^2a
=1-sinacosa=右边
2求证(2-cos^2a)(1+2cot^2a)=(2+cot^2a)(2-sin^2a)
左边=(2-cos^2a)(sin^2a+2cos^2a)/sin^2a
右边=(2sin^2a+cos^2a)(2-sin^2a)/sin^2a
显然:左边=右边
3已知tana=-1/2求下列式子等于多少
得:cosa=-2sina
因为:sin^2a+cos^2a=1
所以:sin^2a=1/5
1 sin^2a-2sinacosa-cos^2a/4cos^a-3sin^2a+1
=1/18
2 sin^2a-3sinacosa-1
=2/5
3.1/4sin^2a+2/5cos^2a
=37/100