The solution set of the equation 2sin2x+√3cosx+1=0 is {2nπ±aπb,n∈Z;ab∈[0,1]} where a,b are co-prime. Then the value of a+b is
A
10
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B
11
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C
9
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D
15
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Solution
The correct option is B11 2sin2x+√3cosx+1=0⇒2(1−cos2x)+√3cosx+1=0⇒2cos2x−√3cosx−3=0⇒(2cosx+√3)(cosx−√3)=0 ⇒cosx=−√32 or cosx=√3 (not possible) ⇒cosx=cos5π6 ⇒x∈{2nπ±5π6,n∈Z} ∴a=5 and b=6 ⇒a+b=11