Number of solutions of 3 cos2 +8 cosθ+3 3=0 , ∈ [-3 ,2 ] is:

Question

Accepted Answer

Correct answer: B. (b) Using cos2 =2 cos^2 -1 : 2 3 cos^2 +8 cosθ+2 3=0 ⇒ 3 cos^2 +4 cosθ+ 3=0. cosθ= -4 22 3, giving cosθ=- 1 3 or cosθ=- 3 (rejected). Let = cos^-1 (-1/ 3 ) ≈2.186 rad. General solution: =2 nπ . In [-3 ,2 ] : = ,- ,2 - ,-2 + ,-2 - . Total =5 solutions.

$Number of solutions of 3 cos 2 θ + 8 cosθ + 33 = 0, θ \in [- 3 π, 2 π] is:$

Solution

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