MHT CET · Maths · Trigonometric Equations
The possible values of \(\theta \in(0, \pi)\) such that \(\sin \theta+\sin (4 \theta)+\sin (7 \theta)=0\) are
- A \(\frac{\pi}{4}, \frac{5 \pi}{12}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)
- B \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{35 \pi}{36}\)
- C \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{10}\)
- D \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)
Step-by-step Solution
Detailed explanation
\(\sin \theta+\sin (7 \theta)+\sin (4 \theta)=0\) \(2 \sin \left(\frac{\theta+7 \theta}{2}\right) \cos \left(\frac{\theta-7 \theta}{2}\right)+\sin (4 \theta)=0\)
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
- If is the inverse function of and then isMHT CET 2017 Medium
- If the vectors \(\hat{i}+2 \hat{\jmath}+x \hat{k}\) and \(y t+6 \hat{k}+4 \hat{k}\) are collinear, then the values of \(x\) and
\(y\) are respectively,MHT CET 2020 Easy - Locus of the point of intersection of perpendicular tangents to the circle \(x^{2}+y^{2}=16\) isMHT CET 2009 Medium
- If planes and pass through a straight line thenMHT CET 2018 Hard
- A fair die is tossed twice in succession. If \(\mathrm{X}\) denotes the number of fours in two tosses, then the probability distribution of \(\mathrm{X}\) is given byMHT CET 2023 Hard
- The number of distinct real values of \(\lambda\), for which the vectors \(-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}-\lambda^2 \hat{k}\) are coplanar, isMHT CET 2024 Easy
More PYQs from MHT CET
- Identify the product formed when bauxite ore is treated with sodium hydroxide?MHT CET 2020 Easy
- MHT CET 2019 Hard
- A pipe open at both ends has length \(1 \mathrm{~m}\). The air column in the pipe can not resonate for a frequency (Neglect end correction, speed of sound in air \(=340 \mathrm{~m} / \mathrm{s}\) )MHT CET 2020 Medium
- In hydrarch succession, the reed swamp stage comes immediately after ________.MHT CET 2025 Medium
- If \((2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0\) and \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)\) isMHT CET 2023 Medium
- Which element from following rapidly loses its luster in air and tarnishes?MHT CET 2023 Easy