Draw a triangle rectangle which sides are and so , etc.
1)I'm supposed to simplify:
Sin ( ArcCot (Sec (ArcTan (x) ) ) )
It's been a while since I've had to do these and I can't remember how to start.
2) Show that ArcSin ((x-1)/(x+1)) = 2 ArcTan (x^(1/2) - pi/2)
I have no clue on this one...
Not looking for answers per say, but ideas on what direction to take...
Make a substitution. Let u= what's inside. So in (1), let
. From that you have a triangle
since this means that . So, u is an angle in your right triangle, and not the right angle, tangent is opposite over hippopotamus. So draw it with x as the length of the opposite side and 1 as your hippo.
Figure out that other side by . Then get sec U....