Q: The value of (2 ^ -1 x+ ^ -1 x ) at x= 1 5 is

aligned & [2 ^ -1 x+ ^ -1 x ] \\ & = [ ^ -1 x+ ^ -1 x+ ^ -1 x ] \\ & = [ ^ -1 x+ / 2 ]=- [ ^ -1 x ] \\ & =- [ ^ -1 1-x^2 ]=- 1-x^2 \\ & =- 1- ( 1 5 )^2 =- 24 25 =- 2 6 5 \\ & aligned

Q: The value of (2 ^ -1 x+ ^ -1 x ) at x= 1 5 is

[2 ^ -1 x+ ^ -1 x ] = [ ^ -1 x+ ^ -1 x+ ^ -1 x ] = [ ^ -1 x+ 2 ]=- [ ^ -1 x ] =- [ ^ -1 1-x^ 2 ]=- 1-x^ 2 =- 1- ( 1 5 )^ 2 =- 24 25 =- 2 6 5

Question 1

If ( ^ -1 x )= \ ^ -1 ( a b^2-a^2 ) \ b a, then x =

Accepted Answer

Given that, ( ^ -1 x )= \ ^ -1 ( a b^2-a^2 ) \ Since, ^ -1 x= ^ -1 ( x 1-x^2 ) and ^ -1 x= ^ -1 ( 1+x^2 ) ( ^ -1 x 1-x^2 )= \ ^ -1 1+ ( a b^2-a^2 )^2 \ x 1-x^2 = b^2-a^2+a^2 b^2-a^2 x 1-x^2 = b b^2-a^2 On squaring both the sides, we get x^2 1-x^2 = b^2 b^2-a^2 aligned & x^2 b^2-x^2 a^2=b^2-b^2 x^2 \ & x^2 b^2+b^2 x^2-x^2 a^2=b^2 aligned 2 x^2 b^2-x^2 a^2=b^2 x^2 (2 b^2-a^2 )=b^2 x= b 2 b^2-a^2

Question 2

If ^ -1 ( 1 2 )= ( ^ -1 x ), then the value of x is

Accepted Answer

We have ( ^ -1 ( 1 2 ) )= ( ^ -1 x ) Let ^ -1 ( 1 2 )= = 1 2 ^ -1 1 5 ( ^ -1 1 5 )= ( ^ -1 x 1-x^2 ) 1 5 = x 1-x^2 1-x^2 = 5 x On squaring both sides, we get, 1-x^2=5 x^2 1=6 x^2 x= 1 6 array ll & x= 1 6 [neglecting - ve sign] array

Question 3

The value of (2 ^ -1 x+ ^ -1 x ) at x= 1 5 is

Accepted Answer

aligned & [2 ^ -1 x+ ^ -1 x ] \ & = [ ^ -1 x+ ^ -1 x+ ^ -1 x ] \ & = [ ^ -1 x+ / 2 ]=- [ ^ -1 x ] \ & =- [ ^ -1 1-x^2 ]=- 1-x^2 \ & =- 1- ( 1 5 )^2 =- 24 25 =- 2 6 5 \ & aligned

Question 4

^ -1 ( 1 4 )+ ^ -1 ( 2 9 ) is equal to

Accepted Answer

^ -1 ( 1 4 )+ ^ -1 ( 2 9 )= ^ -1 \ 1 4 + 2 9 1- 1 4 2 9 \ = ^ -1 \ 9+8 36-2 \ = ^ -1 ( 1 2 )

Question 5

If x (0, 2 ) then the value of ^ -1 ( 7 2 (1+ 2 x)+ ( ^2 x-48 ^2 x ) x ) is equal to

Accepted Answer

y= ^ -1 ( 7 2 (1+ 2 x)+ ( ^2 x-48 ^2 x ) x ) = ^ -1 ((7 x)( x)+ 1-49 ^2 x 1- ^2 x ) = ^ -1 ( x)- ^ -1 (7 x) [ x < 7 x] =x- ^ -1 (7 x)

Question 6

The value of (2 ^ -1 x+ ^ -1 x ) at x= 1 5 is

Accepted Answer

[2 ^ -1 x+ ^ -1 x ] = [ ^ -1 x+ ^ -1 x+ ^ -1 x ] = [ ^ -1 x+ 2 ]=- [ ^ -1 x ] =- [ ^ -1 1-x^ 2 ]=- 1-x^ 2 =- 1- ( 1 5 )^ 2 =- 24 25 =- 2 6 5

Inverse Trigonometric Functions — Previous Year Questions & Solutions