What is the transformation that maps y=cosX on to y=cos1/2 X?

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Answer 1 · 2016-07-07T02:12:02

Transformed y= $sqrt$ ((1+ $given$ y)/2).

Use $cos (x/2)=sqrt((1+cos x)/2)$ .

Here for reading $cos x$ as $cos (x/2)$ , instead, $y to sqrt((1+y)/2)$ .

For checking, use inverse mapping, after transformation

$y= cos (x/2)$ . Inversely,

$x = 2 cos^(-1) y= 2 cos^(-1$ (transformed y)

$=2cos^(-1)sqrt$ ((1+ given y)/2))

$=2cos^(-1)sqrt((1+cos x)/2)$

$=2cos^(-1)cos (x/2)=2(x/2)=x.$