2.6.2 Greatest hits from previous weeks

2.6.2.1 Understanding differences between Maple and Mathematica in examples picked by Maplesoft

http://mathematica.stackexchange.com/questions/60124/understanding-differences-between-maple-and-mathematica-in-examples-picked-by-ma

 
I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? 
 
MAPLE: 
 
 
 
MATHEMATICA: 
 
 
 
Also on page 17  ...
 

- asked by mrz (31 votes), answered by Mr.Wizard (37 votes)

2.6.2.2 How to express trigonometric equation in terms of of given trigonometric function?

http://mathematica.stackexchange.com/questions/434/how-to-express-trigonometric-equation-in-terms-of-of-given-trigonometric-functio

 
How can I express a trigonometric equation / identity in terms of a given trigonometric function? 
 
using following trigonometric identities 
 
Sin[x]^2+Cos[x]^2==1 
Sin[x]/Cos[x]==Tan[x] 
...
 

- asked by Prashant Bhate (23 votes), answered by Simon (27 votes)