UPSEE Solved Model Paper 4

A - B =

1

π

[

sin−1(πx)	tan−1( π x )
sin−1( π x )	tan−1(πx)

] -

1

π

[

−cos−1(πx)	tan−1( π x )
sin−1( π x )	−tan−1(πx)

]
⇒ π (A - B) =

1

π

[

sin−1(πx)	tan−1( π x )
sin−1( π x )	tan−1(πx)

] - [

−cos−1(πx)	tan−1( π x )
sin−1( π x )	−tan−1(πx)

]
⇒ π (A - B) =
Subtract the corresponding elements
⇒ π (A - B) = [

π 2	0
0	π 2

] , use the identities
sin−1x+cos−1x =

π

2

= tan−1x+cot−1x
⇒ π (A - B) =

π

2

[

1	0
0	1

] =

π

2

I , take

π

2

common
∴ A - B =

1

2

I