Draw the graph of `y=(sin2x)sqrt(1+tan^2x)` , find its domain and range.

Answer

Domain: `R-{(2n+1)(pi)/(2), n in Z}`
Range: (-2, 2)

Explanation

`y=(sin2x)sqrt(1+tan^(2)x)`
`=(2sinxcosx)|sec x|`
`={(2sinx",",cosx gt 0),(-2sinx",",cosx lt 0):}`
`={(2sinx",",x in "1st and 4th quadrant"),(-2sinx",",x in "2nd and 3rd quadrant "):}`
The graph of the shown in the following figure.

From the graph, range of the function is `(-2,2).`