Question

Verify the identity. (Simplify at each step.) $$ \tan \left(\sin ^{-1}\left(\frac{x-1}{2}\right)\right)=\frac{x-1}{\sqrt{4-(x-1)^{2}}} $$ Let $$ \theta=\sin ^{-1}\left(\frac{x-1}{2}\right) \Rightarrow \sin (\theta)=\frac{x-1}{2} $$ $$ \tan \left(\sin ^{-1}\left(\frac{x-1}{2}\right)\right)=\tan (\quad) $$ $$ = $$ $$ = \frac{2}{\sqrt{4-(x-1)^{2}}} $$ $$ = \frac{x-1}{\sqrt{4-(x-1)^{2}}} $$

Name: verify the identity simplify at each step tan leftsin 1leftfracx 12rightrightfracx 1sqrt4 x 12 let thetasin 1leftfracx 12right rightarrow sin thetafracx 12 tan leftsin 1leftfracx 12rightrigh 07196
Uploaded: 2022-03-22T16:52:09-08:00
Duration: 1 min 32 s
Channel: Julie Silva
Description: verify the identity simplify at each step tan leftsin 1leftfracx 12rightrightfracx 1sqrt4 x 12 let thetasin 1leftfracx 12right rightarrow sin thetafracx 12 tan leftsin 1leftfracx 12rightrigh 07196

          Verify the identity. (Simplify at each step.)
$$ \tan \left(\sin ^{-1}\left(\frac{x-1}{2}\right)\right)=\frac{x-1}{\sqrt{4-(x-1)^{2}}} $$
Let $$ \theta=\sin ^{-1}\left(\frac{x-1}{2}\right) \Rightarrow \sin (\theta)=\frac{x-1}{2} $$
$$ \tan \left(\sin ^{-1}\left(\frac{x-1}{2}\right)\right)=\tan (\quad) $$
$$ = $$
$$ = \frac{2}{\sqrt{4-(x-1)^{2}}} $$
$$ = \frac{x-1}{\sqrt{4-(x-1)^{2}}} $$

$verify the identity simplify at each step tan leftsin 1leftfracx 12rightrightfracx 1sqrt4 x 12 let thetasin 1leftfracx 12right rightarrow sin thetafracx 12 tan leftsin 1leftfracx 12rightrigh 07196$

Added by Ann F.

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