1.

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

Answer» Correct Answer - C
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.


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