Lishifu

Interesting article XD. Indeed, in communities where young, educated Chinese women congregate, little puppies are preferred. "The growing interest in little puppies is partly a reflection of the changing socioeconomic status of women in China. A survey conducted early this year found that although Chinese women are still earning 22% less than men on average, the gap is narrowing, with the difference at 30% the year before. Modern Chinese women living in major cities care less and less about finding a “proper match,” at least in terms of wealth." https://qz.com/1287606/introducing-little-puppies-the-ideal-boyfriend-type-for-chinas-young-women/?utm_source=parSHG

This one was pretty easy compared to the previous 2, well it involved the same identity as the 1st one which i solved, so no time waste in finding those identities XD and the solving was quick. The answer is 4×sina×sinb×cosc/sina×sinb×cosc.. ie. Simply 4. (felt bad writing just a number as an answer lol)

The creators of chaos theory had a special mathematical ability! Each one of them from the ones who started it to its progressors, all of them were bad at maths. Actually not! They just had a different way of solving mathematics, they could take any equation, no matter how much complex it was or how much power it has and convert it into a multi-dimensional(more than 3) graph in their mind, then cut that graph into various segments and see the answer through those segments! They relied on this and were bad at the traditional methods of solving problems! As a result they became very weak at solving relatively simpler problems but could solve complex and extremely complex problems at ease. As if they were made to tackle the chaos! Each one of them were shunned by mathematecians and physists untill they gave birth to their own field.. chaos theory.

https://youtu.be/s86-Z-CbaHA The Banach–Tarski Paradox: According to it mathematically it is possible to split a real physical object into multiple parts.. and combine them to obtain 2 copies of the original object!! No loss of mass, no loss of matter! simply speaking 1 + 1 = 1 This is not possible in our world though coz maybe we lack the technology to do it? dont know.. But theoretically it SHOULD BE POSSIBLE! Such interesting things can only happen in maths >.>

http://a.nime.me/0116/3369/img_6577.png ^this question was really difficult ^^ Finding the upper limit was very easy, where i got stuck was finding the lower limit.. and its no wonder i got stuck there as i needed a derivative identity this time which i didnt know and had to work that out from scratch -_- it was still fun XD the answer is all numbers from range of e to 7.. (e being the lower limit and 7 the upper limit)