`(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1` if

Options

A. `theta in (0, pi/2)`
B. `theta in (pi/2, pi)`
C. `theta in (pi, (3pi)/2)`
D. `theta in ((3pi)/2, 2pi)`

Answer

B

Explanation

`(sin^(2) theta+cos^(2) theta+ sin theta cos theta)- (cos theta)/(|cosec theta|)-2=-1`
or `1+sin theta cos theta -|sin theta| cos theta-1=0`
or `cos theta (sin theta -|sin theta|)=0`
`rArr theta in (0, pi/2) or theta in (pi/2, pi)`
But `theta ne pi/4` (not in domain), therefore, `theta in (pi/2, pi)`