Question

(sin²a-sin²b)/(sina·cosa-sinb·cosb) 如何化简，求详细步骤

Answer 1

(sin²a-sin²b)/(sina·cosa-sinb·cosb) = (sin a-sin b)(sin a+sin b)/(sin(a-b)) = 2*(cos (a+b)/2)*(sin (a-b)/2)*2*(sin (a+b)/2)*(cos (a-b)/2)/(2*sin((a-b)/2)*cos((a-b)/2))=2*(cos(a+b)/2)*(sin(a+b)/2) = sin(a+b)

用到了和差化积

追问

亲sina.cosa-sinb.cosb 不等于sin(a-b)吧，但是能回答就给赞了

追答

哦 公式记错了 那下面也用和差化积 sina*cosa-sinb*cosb = 1/2sin 2a - 1/2sin 2b = 1/2*(2*(cos(2a+2b)/2)*(sin(2a-2b)/2)) = cos(a+b)*sin(a-b) 上面不动 最后结果是tan(a+b)