arcsin2X+arcsinX=Pi/2 I dont know where to start or how to do any of it! Plase Help!!! Thanks
A adpcane15 New member Joined Apr 12, 2007 Messages 12 Apr 29, 2007 #1 arcsin2X+arcsinX=Pi/2 I dont know where to start or how to do any of it! Plase Help!!! Thanks
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Apr 29, 2007 #2 \(\displaystyle \L\\sin^{-1}(2x)+sin^{-1}(x)=\frac{\pi}{2}\) IDENTITY: \(\displaystyle \frac{\pi}{2}-sin^{-1}(x)=cos^{-1}(x)\) \(\displaystyle \L\\sin^{-1}(2x)=cos^{-1}(x)\) \(\displaystyle \L\\2x=sin(cos^{-1}(x))\) \(\displaystyle \L\\2x=\sqrt{1-x^{2}}\) Now, finish?.
\(\displaystyle \L\\sin^{-1}(2x)+sin^{-1}(x)=\frac{\pi}{2}\) IDENTITY: \(\displaystyle \frac{\pi}{2}-sin^{-1}(x)=cos^{-1}(x)\) \(\displaystyle \L\\sin^{-1}(2x)=cos^{-1}(x)\) \(\displaystyle \L\\2x=sin(cos^{-1}(x))\) \(\displaystyle \L\\2x=\sqrt{1-x^{2}}\) Now, finish?.
