MHT CET · Maths · Trigonometric Equations
The principal solutions of \(\cos 2 x=\frac{-1}{2}\) are
- A \(x=\frac{-2 \pi}{3}, x=\frac{4 \pi}{3}\)
- B \(x=\frac{\pi}{3}, \quad x=\frac{2 \pi}{3}\)
- C \(x=\frac{-\pi}{3}, \quad x=\frac{5 \pi}{6}\)
- D \(x=\frac{\pi}{3}, \quad x=\frac{7 \pi}{6}\)
Answer & Solution
Correct Answer
(B) \(x=\frac{\pi}{3}, \quad x=\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\cos 2 x=\frac{-1}{2} \)
\( \therefore \frac{-1}{2}=\cos \left(\pi-\frac{\pi}{3}\right)-\cos \left(\pi+\frac{\pi}{3}\right) \Rightarrow \frac{-1}{2}-\cos \frac{2 \pi}{3}-\)\(\cos \frac{4 \pi}{3} \)
\( \therefore 2 x=\frac{2 \pi}{3} \text { or } 2 x=\frac{4 \pi}{3} \Rightarrow x=\frac{\pi}{3} \text { or } \frac{2 \pi}{3}\)
\( \therefore \frac{-1}{2}=\cos \left(\pi-\frac{\pi}{3}\right)-\cos \left(\pi+\frac{\pi}{3}\right) \Rightarrow \frac{-1}{2}-\cos \frac{2 \pi}{3}-\)\(\cos \frac{4 \pi}{3} \)
\( \therefore 2 x=\frac{2 \pi}{3} \text { or } 2 x=\frac{4 \pi}{3} \Rightarrow x=\frac{\pi}{3} \text { or } \frac{2 \pi}{3}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The area of the region bounded by the parabola \(y^{2}=8 x\) and its latus rectum isMHT CET 2020 Medium
- A fair coin is tossed 100 times. The probability of getting a head for even number of times isMHT CET 2021 Medium
- The differential equation of the circles having their centres on the line \(\mathrm{y}=8\) and touching the \(\mathrm{X}\) -axis isMHT CET 2020 Medium
- Let \(f(x+y)=f(x) \cdot f(y), \forall x, y \in R\), suppose that \(f(3)=3\) and \(f^{\prime}(0)=11\), then \(f^{\prime}(3)\) is given byMHT CET 2011 Easy
- \(\lim _{x \rightarrow 0} \frac{\left(7^x-1\right)^4}{\tan \left(\frac{x}{\mathrm{k}}\right) \cdot \log \left(1+\frac{x^2}{3}\right) \cdot \sin 4 x}=3(\log 7)^3\)MHT CET 2025 Hard
- The co-ordinates of the points on the line \(\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}\) at a distance of 12 units from the point \(\mathrm{A}(-2,1,-1)\) areMHT CET 2021 Medium
More PYQs from MHT CET
- The excess of pressure, due to surface tension, on a spherical liquid drop of radius ‘R’ is proportional toMHT CET 2019 Easy
- In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respectively are
MHT CET 2024 Medium - If \(\mathrm{E}^{\circ}\left(\mathrm{Ag}^{+}{ }_{(\mathrm{aq})} \mid \mathrm{Ag}_{(\mathrm{s})}\right)=+0.80 \mathrm{~V}\)
What is potential developed for \(\mathrm{Ag}_{(\mathrm{s})} \rightarrow \mathrm{Ag}^{+1}(0 \cdot 01 \mathrm{M})+\overline{\mathrm{e}}\) at 298 K ?MHT CET 2025 Medium - A firm is manufacturing 2000 items. It is estimated that the rate of change of production \(P\) with respect to additional number of workers \(x\) is given by \(\frac{d p}{d x}=100-12 \sqrt{x}\). If the firm employs 25 more workers, then the new level of production of items isMHT CET 2022 Easy
- If \(|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5\), then \(|\bar{a}+\bar{b}|=\)MHT CET 2021 Easy
- With an alternating voltage source of frequency ' \(\mathrm{f}\) ', inductor ' \(\mathrm{L}\) ', capacitor ' \(\mathrm{C}\) ' and resistance ' \(\mathrm{R}\) ' are connected in series. The voltage leads the currently by \(45^{\circ}\). The value of ' \(L\) ' is ( \(\left.\tan 45^{\circ}=1\right)\)MHT CET 2022 Hard