If Cos x = -√3/2 and π < x < 3π/2, then the value of 2Cot2x + 3Cosec2x is:
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Correct answer: D
Explanation
The Correct Answer is option 4 i.e. 18.
Given that
Cos x = -√3/2 and π < x < 3π/2
Hence,
x = 7π/6 = 210°
Cos 210° = Cos(180 + 30) = -Cos 30°= -√3/2
Cot 210° = Cot(180 + 30) = Cot 30°= √3
Cosec 210° = Cosec(180 + 30) = -Cosec 30° = -2
Now,
2Cot2x + 3Cosec2x
Put x = 60°
⇒ 2 × 3 + 3 × (-2)2
⇒ 6 + 12 = 18