Question

求详细过程数学

Answer 1

1. tan (A+B) = sin(A+B) / cos (A+B)

sin(A+B) = sinA * cosB + cosA * sinB   @1

cos(A+B) = cosA * cosB - sinA * sinB   @2

tan(A+B)的分子分母同时除以(cosA * cosB)

@1  / (cosA * cosB) = tanA + tanB  @3

@2 /  (cosA * cosB) = 1 - tanA * tanB @4

tan(A+B) = @1 / @2 = @3 / @4 = (tanA + tanB) / (1 - tanA*tanB)

                = (2 + 1) / ( 1 - 2 * 1) = - 3

2.

sin2A = 2 * sinA * cosA

cos2A = cosA * cosA - sinA * sinA

分子分母同时除以sinA * cosA

分子：

2

分母：

tanA + 1 - 1/tanA + tanA - 1 = 2 * tanA - 1/tanA = 2*2 - 1/2 = 7 / 2

则答案为 4 / 7

不知道我讲的清不清楚，答案应该是这样的，至少过程应该没错