MHT CET · Maths · Trigonometric Equations
The principal solutions of \(\sqrt{3} \sec x+2=0\) are
- A \(\frac{\pi}{6}, \frac{5 \pi}{6}\)
- B \(\frac{5 \pi}{6}, \frac{7 \pi}{6}\)
- C \(\frac{\pi}{3}, \frac{2 \pi}{3}\)
- D \(\frac{2 \pi}{3}, \frac{4 \pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{5 \pi}{6}, \frac{7 \pi}{6}\)
Step-by-step Solution
Detailed explanation
\(\sqrt{3} \sec x+2=0 \)
\( \therefore \sec x=\frac{-2}{\sqrt{3}} \Rightarrow \cos x=\frac{-\sqrt{3}}{2} \)
\( \therefore \cos x=\cos \left(\pi-\frac{\pi}{6}\right)=\cos \left(\pi+\frac{\pi}{6}\right)\) \(\Rightarrow x=\frac{5 \pi}{6}, \frac{7 \pi}{6}\)
\( \therefore \sec x=\frac{-2}{\sqrt{3}} \Rightarrow \cos x=\frac{-\sqrt{3}}{2} \)
\( \therefore \cos x=\cos \left(\pi-\frac{\pi}{6}\right)=\cos \left(\pi+\frac{\pi}{6}\right)\) \(\Rightarrow x=\frac{5 \pi}{6}, \frac{7 \pi}{6}\)
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