Question

If `y=sin^(-1)(sin x),` then `dy/dx` at `x =pi/2` is
A. 1
B. -1
C. non-exisent
D. none of these

Answer 1

Correct Answer - C
We have,
`y=sin^(-1)(sinx)={{:(x" ,",-(pi)/(2)lexle(pi)/(2)),(pi-x",",(pi)/(2)lexle(3pi)/(2)),(x-2pi",",(3pi)/(2)lexle2pi" and so on "):}`
We observe that
`("LHD at "x=pi//2)=1" and "("RHD at "x=pi//2)=-1`
`Hence, `((dy)/(dx))_(x=pi//2)"does not exist"`.