Let S={xϵ(−π,π):x≠0,±π2}. The sum of all distinct solutions of the equation √3secx+cosecx+2(tanx−cotx)=0 in the set S is equal to
A
−7π9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
−2π9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
5π9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C0 √3secx+cosecx+2(tanx−cotx)=0⇒√32sinx+12cosx=cos2x−sin2x⇒cos(x−π3)=cos2x⇒x−π3=2nπ±2x⇒x=2nπ3+π9orx=−2nπ−π3
For xϵS,n=0⇒x=π9,−π3 n=1⇒x=7π9;n=−1⇒x=−5π9 ∴ Sum of all values of x=π9−π3+7π3−5π9=0