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Question

Let S={xϵ(π,π):x0,±π2}. The sum of all distinct solutions of the equation 3sec x+cosec x+2(tan xco tx)=0 in the set S is equal to

A
7π9
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B
2π9
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C
0
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D
5π9
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Solution

The correct option is C 0
3secx+cosecx+2(tanxcotx)=032sin x+12cosx=cos2xsin2xcos(xπ3)=cos2xxπ3=2nπ±2xx=2nπ3+π9 or x=2nππ3
For xϵS,n=0x=π9,π3
n=1x=7π9;n=1x=5π9
Sum of all values of x=π9π3+7π35π9=0

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