Question

まさっち

次の計算をしなさい

-sinπ/12＋√3cosπ/12

どなたか教えてください。

Answer 1

LUX SIT

係数に気をつけると上手く解けます.
2{(-1/2)sin(π/12)+(√3/2)cos(π/12)} [三角関数の合成を逆に使う. √{(-1)^2+(√3)^2}=2]
=2sin(π/12+2π/3) [cosα=-1/2, sinα=√3/2となるαは2π/3]
=2sin(3π/4)=2*(1/√2)=√2.

Answer 2

KONTON

三角関数の合成を使います。
2[sinπ/12×(-1/2)+cosπ/12×(√3/2)]
=2(sinπ/12×cos2π/3+cosπ/12×sin2π/3)
=2sin(π/12+2π/3)
=2sin3π/4
=2×√2/2
=√2