Consider the cubic equation `x^3-(1+cos theta+sin theta)x^2+(cos theta sin theta+cos theta+sin theta)x-sin theta. cos theta =0` Whose roots are `x_1, x_2 and x_3`

Options

A. 3
B. 4
C. 5
D. 6

Answer

C

Explanation

Now if `1=sin theta`, we get `theta=pi//2`
If `1= cos theta`, then `theta=0, 2pi` and if `sin theta=cos theta`, we get `tan theta=1`.
therefore,
`theta=pi/4, (5pi)/4`
Therefore, the number of values of `theta` in `[0, 2pi]` is 5.