Question

Verify the Trigonometry Identity. Appreciate the help! :D

Answer 1

\[2\tan(\cos^-1 (x+1)/2)=(\sqrt{16-4(x+1)^2})/(x+1)\]

Answer 2

cos^-1=arccos

Answer 3

okay so this requires a few trig identities.

Answer 4

\[1+\tan^2(b)=\sec^2(b)=\frac{ 1 }{ \cos^2(b) }\]

Answer 5

where

\[b=\cos^{-1}(\frac{x+1}{2})\]

Answer 6

Now we take the cos of both sides to obtain:

\[\cos(b)=\frac{x+1}{2}\]

Answer 7

Plug that into the trig identity above:

\[1+\tan^2(b)=\frac{1}{\cos^2(b)}=\frac{1}{(\frac{x+1}{2})^2}\]

Answer 8

Can you see where to go from here?