If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5sin^(2theta)+1)=pi/2,` then value of `2cos^2theta-sintheta` is equal to 0 (b) `-1` (c) `1` (d) none of these

Options

A. 0
B. `-1`
C. 1
D. none of these

Answer

C

Explanation

From the given equation `sin^(2) theta - 2 sin theta + 3 = 5^("sec"^(2)y) + 1`, we get
`(sin theta -1)^(2) + 2 = 5^("sec^(2)y) + 1`
`L.H.S. le 6, R.H.S. ge 6`
Possible solution is `sin theta = -1` when L.H.S. = R.HgtS.
`rArr cos^(2) theta = 0`
`rArr cos^(2) theta - sin theta = 1`