Question

sin6度cos24度sin78度cos48度怎么算.②1/sin10 +根号3/cos10

Answer 1

(I).sin78°=cos12°
sin6°cos24°sin78°cos48°
= sin6°cos12°cos24°cos48° 先乘以cos6°,再除以cos6°,结袭岩卖果不变
= (sin6°cos6°cos12°cos24°cos48°)/cos6° 多次应用二枣唤倍角公式
= (1/2*sin12°cos12°cos24°cos48°)/cos6°
= (1/4*sin24°cos24°cos48°)/cos6°
= (1/8*sin48°cos48°)/cos6°
= 1/16 *sin96°/cos6°
= 1/16 *sin84°/cos6°
= 1/16 *cos6/cos6°
= 1/16
(II) 1/sin10° +根号3/cos10° 通分
= (1*cos10° +根号3*sin10°)/sin10°cos10° 上面用辅助角公式,下面用二倍角公式
= 2*sin(10°+30°)/[1/2*sin20°]
= 4*sin40°/sin20° 二倍角公拍逗式
= 8*sin20°*cos20°/sin20°
= 8cos20°