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 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 these
Answer» `[cot^-1x]+[cos^-1x] = 0` As, `cot^-1x and cos^-1 x ge 0`, So, only solution available for this equation is, `[cot^-1x] = [cos^-1x] = 0` When `[cot^-1x] = 0, x in (cot1,oo)` When `[cos^-1x] = 0, x in (cos1,1)` Intersection of above two cases will be `x in (cot 1, 1)`. So, option `c` is the correct option.

`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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