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The sum of all the solutions of cottheta...

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`

A

`3pi//2`

B

`pi`

C

`3pi//4`

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
A
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`.
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