Find the set of values of k for which ` x^(2) - kx + sin^(-1) ( sin 4) gt 0 ` for all real x .

Options

A. `phi`
B. `(-2,2)`
C. R
D. none of these

Explanation

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