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If theta in R - {(4n + 1) pi/4 , n in I}...

If `theta in R - {(4n + 1) pi/4 , n in I}` , then range of `(cos 3 theta + sin 3 theta)/(cos theta - sin theta)` is :

A

`[-1, 3]`

B

`[-1, 3)`

C

`[1, 3)`

D

`[-2,2]`

Text Solution

Verified by Experts

The correct Answer is:
B

`(cos 3 theta + sin 3 theta)/(cos theta - sin theta) = (4 cos^3 theta - 3 cos theta + 3 sin theta - 4 sin^3 theta)/(costheta - sin theta)`
`= 4 (cos^2 theta + sin^2 theta + sin theta cos theta) - 3, cos theta != sin theta = 1 + 2 sin 2 theta in [-1, 3)`.
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