Put together sine and cosine of the same angle : tcollect tCollect

tcollect or tCollect takes as argument an expression containing trigonometric functions.
tcollect first linearizes this expression (e.g. in terms of sin(n.x) and cos(n.x)), then, puts together sine and cosine of the same angle.
Input :

tcollect(sin(x)+cos(x))

Output :

sqrt(2)*cos(x-pi/4)

Input :

tcollect(2*sin(x)*cos(x)+cos(2*x))

Output :

sqrt(2)*cos(2*x-pi/4)