we are given
[tex]sin^{-1}(tan(\frac{\pi}{4}))[/tex]
Let's assume entire term as x
[tex]sin^{-1}(tan(\frac{\pi}{4}))=x[/tex]
now, we can take both sides as sin
[tex]sin(sin^{-1}(tan(\frac{\pi}{4})))=sin(x)[/tex]
since, sin and sin^-1 are inverse of each other
so, they will get cancelled
and we get
[tex]tan(\frac{\pi}{4})=sin(x)[/tex]
now, we know that
tan(pi/4)=1
[tex]1=sin(x)[/tex]
and sin is 1 at pi/2
so, we get
[tex]x=\frac{\pi}{2}[/tex]
so, option-D.........Answer
