几道高一数学题~恳请牛人相助1.函数y=1/sinx+1/cosx+1/(sinxcosx),x∈(0,pie/2),最小值是多少?2.已知a,b是锐角,且3(sina)^2+2(sinb)^2=1,3sin2a-2sin2b=0,求证：a+2b=pie/2.3.计算3/(sin20度)^2-1/(cos20度)^2+64(sin20度)^2暂时这三道.最好有详细的步骤,谢了.
2019-06-25
几道高一数学题~恳请牛人相助
1.函数y=1/sinx+1/cosx+1/(sinxcosx),x∈(0,pie/2),最小值是多少?
2.已知a,b是锐角,且3(sina)^2+2(sinb)^2=1,3sin2a-2sin2b=0,求证：a+2b=pie/2.
3.计算3/(sin20度)^2-1/(cos20度)^2+64(sin20度)^2
暂时这三道.
最好有详细的步骤,谢了.
优质解答
y=1/sinx+1/cosx+1/(sinxcosx)≤2
3(sina)^2+2(sinb)^2=1,3sin2a-2sin2b=0,求证：a+2b=pie/2.
3/(sin20度)^2-1/(cos20度)^2+64(sin20度)^2
=（3 cos^20°- sin^20°）/（ sin^20°cos^20°）+64(sin20度)^2
=（1/4）sin^40°
y=1/sinx+1/cosx+1/(sinxcosx)≤2
3(sina)^2+2(sinb)^2=1,3sin2a-2sin2b=0,求证：a+2b=pie/2.
3/(sin20度)^2-1/(cos20度)^2+64(sin20度)^2
=（3 cos^20°- sin^20°）/（ sin^20°cos^20°）+64(sin20度)^2
=（1/4）sin^40°