If `[cot^(-1)x]+[cos^(-1)x]=0`, where `[]`denotes the greatest integer functions, then the complete set of valuesof `x`is`(cos1,1)`(b) `cos1,cos1)``(cot1,1)`(d) none of theseA. `(cos 1,1]`B. `(cos 1, cot1)`C. `(cot 1, 1]`D. none of these

If `[cot^(-1)x]+[cos^(-1)x]=0`, where `[]`denotes the greatest integer

1.	If `[cot^(-1)x]+[cos^(-1)x]=0`, where `[]`denotes the greatest integer functions, then the complete set of valuesof `x`is`(cos1,1)`(b) `cos1,cos1)``(cot1,1)`(d) none of theseA. `(cos 1,1]`B. `(cos 1, cot1)`C. `(cot 1, 1]`D. none of these
Answer» We have `cot^(-1) x in [0,pi] and cos^(-1) x in [0,pi]` `therefore [cost(-1)x]gt0 and [cos^(-1)x]ge0` Now `[cos^(-1)x]=0 =[cos^(-1)xlt1` `rarr cot 1 ltx lt infty and cos 1 lt x le 1` `rarr fx in (cot1,infty) and x in (cos 1,1]rarr x in (cot1,1]`

`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)`