Question

急求答案数学必修4三角恒定变换

1.y=sin^4x+cos^2x的最小周期
2.sin65+sin15sin10/sin25-cos15cos80的植

Answer 1

（1）y=(sin²x)²-sin²x+1
=-sin²xcos²x+1
=1-(sin²2x)/4
=(cos4x)/8+7/8
T=2π/4=π/2
(2)原式=（cos25°+sin15°sin10°)/(sin25°-cos15°sin10°)
=[cos(15°+10°)+sin15°sin10°]/[sin(15°+10°)-cos15°sin10°]
=cos15°cos10°/(sin15°cos10°)
=cos15°/sin15°
=2cos²15°/(2sin15°cos15°)
=(1+cos30°)/sin30°
=2+√3

Answer 2

y=sin^4-sin^2+1=((1-cos2x)/2)^2-(1-cos2x)/2+1=
cos^2(2x)-1=1-sin^2x/4=7/8+cos4x/8
周期为π/2