问一道向量和三角函数的综合题设向量a=（cos23,sin23) b=(cos53,cos23),则a*b=______

a·b=（cos23,sin23) ·(cos53,cos23)
=cos23cos53+sin23cos23
=cos23cos(30+23)+sin23cos23
=cos23(cos30cos23-sin30sin23+sin23)
=cos23[cos30cos23-(1/2)sin23+sin23]
=cos23[cos30cos23+(1/2)sin23]
=cos23[cos30cos23+sin30sin23]
=cos23cos(30-23)
=cos23cos7
=(1/2)[cos(23+7)+cos(23-7)]
=(1/2)cos30+(1/2)cos16
=√3/4+(1/2)cos16
PS:题目是不是没输入对?要是对的话,结果就是√3/4+(1/2)cos16