Question

求13题解答过程（详细点）

Answer 1

1.sin6°sin42°sin66°sin78°
=sin6°cos12°cos24°cos48°
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16

追问

2，3，4呢

追答

2.

追问

3呢

追答

3.[2sin50°+sin10°(1+√3*tan10°)]√(1+cos20°)
=[2sin50°+sin10°(cos10°+√3*sin10°)/cos10°]√(2cos²10°)
=(√2)*cos10°[2sin50°+2sin10°(1/2 *cos10°+√3/2 *sin10°)/cos10°]
=(√2)*cos10°[2sin50°+2sin10°(1/2 *cos10°+√3/2 *sin10°)/cos10°]
=2√2*[sin50°cos10°+sin10°cos(60°-10°)]
=2√2*(sin50°cos10°+sin10°cos50°)
=2√2*sin（50°+10°）
=2√2*sin60°
=2√2*(√3)/2
=√6

4.原式=-√3(tan60-tan12)/(2sin12cos24)
=-2√3tan48(1+tan60tan12)cos12/sin48
=-4√3(sin30cos12+cos30sin12)/cos48
=-4√3sin42/cos48
=-4√3

追问

4呢