Match the statements in List I with those in List II

1.	Match the statements in List I with those in List II
Answer» Correct Answer - `b rarr p, r` `tan^(-1) (x + 3) - tan^(-1) (x -3) = sin^(-1) (3//5)` `rArr tan^(-1).((x +3)-(x -3))/(1 + (x^(2) -9)) = tan^(-1).(3)/(4)` `rArr (6)/(x^(2) -8) = (3)/(4)` `:. X^(2) -8 = 8` or `x = +- 4` Clearly, both values satisfy the equation Note : Solution of the remaining parts are given in their respective chapters.

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
Find the principal value of `sin^(-1)(-1/sqrt2)-2tan^(-1)(-sqrt3)+cos^(-1)(-1/2)`.
Find the principal value of the following: (i) `cosec^(-1)(2)` (ii) `tan^(-1) (-sqrt3)` (iii) `cos^(-1) (-(1)/(sqrt2))`
The value of the expression `sin^(-1)(sin(22pi)/7)+cos^(-1)(cos(5pi)/3)+tan^(-1)(tan(5pi)/7)+sin^(-1)(cos2)`is(a) `(17pi)/(42)-2`(b) `-2`(c)`(-pi)/(21)-2`(d) `non eoft h e s e`
The domain of definition of f(X) = `sin^(-1)(-x^(2))` isA. `[-1,1]`B. `[0,1]`C. `[-1,0]`D. `[-2,23]`
If `x , y , z in [-1,1]`such that `sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2,`find the value of `x^2+y^2+z^2dot`A. 1B. 3C. `(3pi^(23))/(4)`D. `3pi^(2)`
The domain of definition of `cos^(-1)(2x-1)` isA. `[-1,1]`B. `[0,1]`C. `[-1,0]`D. `[0,2]`
The value of `cos^(-1)(cos(5pi)/3)+sin^(-1)(sin(5pi)/3)`is`pi/2`(b) `(5pi)/3`(c) `(10pi)/3`(d) 0
Find the principal value of `sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)`