MHT CET · Maths · Trigonometric Equations
The principal solutions of the equation \(\sqrt{3} \operatorname{cosec} X+2=0\) are
- A \(\frac{2 \pi}{3}, \frac{5 \pi}{3}\)
- B \(\frac{4 \pi}{3}, \frac{5 \pi}{3}\)
- C \(\frac{\pi}{3}, \frac{2 \pi}{3}\)
- D \(\frac{2 \pi}{3}, \frac{4 \pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{4 \pi}{3}, \frac{5 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sqrt{3} \operatorname{cosec} x+2 \\ & \Rightarrow \sin x=-\frac{\sqrt{3}}{2}=-\sin \frac{\pi}{3} \\ & \Rightarrow x=\pi+\frac{\pi}{3} \text { or } 2 \pi-\frac{\pi}{3} \\ & \Rightarrow x=\frac{4 \pi}{3} \text { or } \frac{5 \pi}{3}\end{aligned}\)
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