CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Test Paper 01
CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Test Paper 01
CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Test Paper 01
Class 12 Mathematics
Chapter 2 Inverse Trigonometric Functions
Test Paper 01
3. Prove that
8. Prove that
9. Show that .
10. Find x if .
1. Let
Principal value is
2. Let
We know that ,
3.
4.
5. We have, .
6. Given:
7.
1 - x = cos(2sin-1x)
1 - x = cos2(sin-1x)
= 1 - 2sin2(sin-1x)
= 1 - 2[sin(sin-1x)]2
1 - x = 1 - 2x2
2x2 - x = 0
x(2x - 1) = 0
x = 0,
8.
RHS =
LHS
LHS =
= RHS
Hence proved
9. Let = sin-1( )
sin =
Since, tan =
Thus,
Similarly,
We have,
LHS =
=
Hence Proved.
10.
1 - x = cos(2sin-1x)
1 - x = cos2(sin-1x)
= 1 - 2sin2(sin-1x)
= 1 - 2[sin(sin-1x)]2
1 - x = 1 - 2x2
2x2 - x = 0
x(2x - 1) = 0
x = 0,