The set of values of k for which `x^2 - kx + sin^-1 (sin 4) > 0` for all real x isA. `phi`B. `(-2,2)`C. RD. none of these

The set of values of k for which `x^2 - kx + sin^-1 (sin 4) > 0` for a

1.	The set of values of k for which `x^2 - kx + sin^-1 (sin 4) > 0` for all real x isA. `phi`B. `(-2,2)`C. RD. none of these
Answer» We have `sin^(-1)(sin4)=sin^(-1)sin(pi-4)=pi-4` `therefore x^(2)-lambdax+sin^(-1)(sin4)gt0` for all `x in R` `rarr x^(2)-lambdax+(pi-4)gt0` for all `x in R` `rarr lambda^(2)-4(pi-4)lt0rarr0lambda^(2)+16-4pi lt 0` But `lambda^(2)+16-4pigt0` But `lambda^(2)+16-4pigt0 for all lambda in R` So there is no value of `lambda` for which the given innequation holds true

`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)`