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If n(1) denotes the maximum number of ro...

If `n_(1)` denotes the maximum number of roots of `sin theta = k_(1)` in `[0,2pi]` and `n_(2)` denotes the maximum number of roots of `cos theta=k_(2)` in `[0,2pi]`, then

A

`n_(1)+n_(2)=5`

B

`n_(1)+n_(2)=4`

C

`n_(1)+n_(2)=6`

D

`n_(1)+n_(2)=3`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin theta = k_(1)` has maximum roots if `k_(1) = 0` , so `theta = pi, pi, 2pi`
`cos theta = k_(2)` has maximum roots if `k_(2) ne pm 1`, so there are two values of `theta`
`therefore n_(1)=3` and `n_(2)=2`
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