Question

已知cos2a/sin(a-π/4)等于-二分之根号六则cos(a-π/4)

Answer 1

问：已知cos2a/sin(a-π/4)等于-二分之根号六则cos(a-π/4)

答：亲亲很高兴为您解答哦,已知cos2a/sin(a-π/4)等于-二分之根号六则cos(a-π/4)等于 (1/√2)(cosa+sin a)

答：亲亲相关拓展：根据三角函数的基本性质，有：cos2a = 2cos²a - 1，sin(a-π/4) = sinacos(π/4) - cosasin(π/4) = (1/√2)(cosa-sina)将上述两个式子代入原式中：cos2a/sin(a-π/4) = [2cos²a - 1] / [ (1/√2)(cosa-sina) ]= [2cos²a - 1] / [ (1/√2)cosa - (1/√2)sina ]。将右侧分母有关sina的项化为一个完全平方数，并用 2sinθcosθ = sin2θ 的公式化简分子得：cos2a/sin(a-π/4) = [2cos²a - 1] / [ √2cos (a + π/4) ]。已知 cos2a/sin(a-π/4) = -√6/2，代入上式并解出cos(a+π/4)得：-√6/2 = [2cos²a - 1] / [ √2cos (a + π/4) ]，cos (a + π/4) = [2cos²a - 1] / (-√3)。再利用 cos(a-π/4) = - sin a

答：可得cos (a - π/4) = - cos(π/2 - (a-π/4)) = - sin(a-π/4) = - (sinacos(π/4) - cosasin(π/4)) = (1/√2)(cosa+sin a)综上所述，cos(a-π/4)等于 (1/√2)(cosa+sin a)。