Absolute value of sum of all integers in the domain of `f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^2+3x+1)`is_______

Absolute value of sum of all integers in the domain of `f(x)=cot^(-1)s

1.	Absolute value of sum of all integers in the domain of `f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^2+3x+1)`is_______
Answer» Correct Answer - `-3` We must have `x(x + 3) ge 0` `rArr x ge 0 " or " x le -3`...(i) Also, `-1 le x^(2) + 3x + 1 le 1` `rArr x(x + 3) le 0 rArr -3 le x le 0`...(ii) From Eqs. (i) and (ii), we get `x = {0, -3}` Also, for these values `x^(2) + 3x + 1 ge -1` Hence, the required sum is `-3`

`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)=`
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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)`
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Find the principal value of `sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)`