The sum of all the solutions of `cottheta=sin2theta(theta!=npi, n in t ege r)` , `0lt=thetalt=pi,` is `(3pi)/2` (b) `pi` (c) 3`pi/4` (d) `2pi`

Options

A. `3pi//2`
B. `pi`
C. `3pi//4`
D. `2pi`

Answer

A

Explanation

From the given relation
`cos theta=(2 sin theta cos theta) sin theta, sin theta ne 0`
`rArr sin theta= pm 1/sqrt(2) or cos theta =0`
`rArr theta= pi/4, (3pi)/4, pi/2" "( :' theta in [0, pi])`
Then the sum of roots is `3pi//2`.