In 0*(10*)*, (10*)* generates all strings on {0,1} except those starting with 0. So if we prefix 0* also then it will include those also. And thus this regex implies (0+1)*.
And now we can see option a in similar way. In (1*0)*1*, (1*0)* generates all strings except those ending with 1, so we prefixed 1* in end. Hence this also follows (1+0)*. Hence option A is the right answer