Question

高一数学选择题图1

Answer 1

一、1.解：答案为D

原式=1/2*(2（sin35°）^2-1)/(cos(10°+80°)+cos(10-80°))/2

=1/2*2*cos70°/cos70°

=1

2.解：答案为A

三角形面积=1/2*AB*AC*sinA

AC=2*三角形面积/(AB*sinA)=2x√3/2x1/2x2/√3=1

3.解：答案为A

cos2α=(cosα)^2-(sinα)^2=(cosα+sinα))(cosα-sinα)

cos(π/4-α)=cosπ/4cosα+sinπ/4sinα

=√2/2cosα+√2/2sinα

=√2/2(cosα+sinα)

∵ cos2α=cos(π/4-α)

∴ (cosα+sinα))(cosα-sinα)=√2/2(cosα+sinα)

∴ cosα-sinα=√2/2

又 ∵ （cosα-sinα）^2=（cosα)^2-2sinαcosα+(sinα)^2=1-sin2α=1/2

∴ 1-sin2α=1/2 sin2α=1-1/2=1/2