Simplifying Trig Functions

**TyrsFromAbove37** · February 25th 2009, 08:29 PM

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...

Any thoughts?

Not looking for answers per say, but ideas on what direction to take...

**Abu-Khalil** · February 25th 2009, 09:24 PM

Draw a triangle rectangle which sides are $x,1$ and $\sqrt{x^2+1}$ so $\text{arcsec} \frac{\sqrt{x^2+1}}{x} =\theta=\arctan x$ , etc.

**matheagle** · February 25th 2009, 09:51 PM

Originally Posted by TyrsFromAbove37

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...

Any thoughts?

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
$u=\arctan x$ . From that you have a triangle
since this means that $\tan u=x/1$ . 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 $a^2+b^2=c^2$ . Then get sec U....

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