If `"sin"^(2) theta -2"sin" theta-1 = 0` is to be satisfied for exactly 4 distinct values of `theta in [0, n pi], n in Z`, then the least values of n, is

Options

A. 2
B. 6
C. 4
D. 1

Answer

D

Explanation

We have,
`"sin"^(2) theta - 2"sin" theta - 1 =0`
`rArr " sin" theta = (2 +- sqrt(4 + 4))/(2)`
`rArr "sin" theta = 1 +- sqrt(2)` ltbrrgt `rArr "sin" theta = 1-sqrt(2) " " [because "sin" theta ne 1 + sqrt(2)]`
This gives two values of `theta "in" [0, 2 pi]` and two values of `theta` in `[2 pi, 4pi]`
Hence, the least value value of n is 4