JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of values of \(\alpha \) in \([0, 2\pi]\) for which \(2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2\) , is
- A \(6\)
- B \(4\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(2 \sin ^{3} \alpha-7 \sin ^{2} \alpha+7 \sin \alpha-2=0\) \(\Rightarrow 2 \sin ^{2} \alpha(\sin \alpha-1)-5 \sin \alpha\) \((\sin \alpha-1)+2(\sin \alpha-1)=0\) \(\Rightarrow(\sin \alpha-1)\left(2 \sin ^{2} \alpha-5 \sin \alpha+2\right)\) \(=0\) \(\Rightarrow \sin \alpha-1=0\)…
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
- Let \(\mathrm{f}: N \rightarrow N\) be a function such that \(\mathrm{f}(\mathrm{m}+\mathrm{n})=\mathrm{f}(\mathrm{m})+\mathrm{f}(\mathrm{n})\) for every \(\mathrm{m}, \mathrm{n} \in N\). If \(\mathrm{f}(6)=18\) then \(\mathrm{f}(2) \cdot \mathrm{f}(3)\) is equal to :JEE Mains 2021 Hard
- The lengths of the sides of a triangle are \(10+ x ^{2}\), \(10+ x ^{2}\) and \(20-2 x ^{2}\). If for \(x = k\), the area of the triangle is maximum, then \(3 K ^{2}\) is equal toJEE Mains 2022 Hard
- If \(5, 5r, 5r^2\) are the lengths of the sides of a triangle, then \(r\) cannot be equal toJEE Mains 2019 Hard
- The total number of functions,\(f:\{1,2,3,4\} \cdot\{1,2,3,4,5,6\}\) such that \(f (1)+ f (2)= f (3)\), is equal to .JEE Mains 2022 Hard
- For \(x \in(-1,1]\), the number of solutions of the equation \(\sin ^{-1} x=2 \tan ^{-1} x\) is equal toJEE Mains 2023 Hard
- Let \(x=x(y)\) be the solution of the differential equation \(y^2 \mathrm{~d} x+\left(x-\frac{1}{y}\right) \mathrm{d} y=0\). If \(x(1)=1\), then \(x\left(\frac{1}{2}\right)\) is :JEE Mains 2025 Hard
More PYQs from JEE Mains
- The range of \(a \in R\) for which the function \( f(x)=(4 a-3)\left(x+\log _{e} 5\right)+2(a-7) \cot \left(\frac{x}{2}\right) \sin ^{2}\left(\frac{x}{2}\right)\) \(x \neq 2 n \pi, n \in N ,\) has critical points, isJEE Mains 2021 Hard
- Let \(f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)\) be a continuous function such that \(f(1-x) = f(x)\) for all \(x \in \left[ { - 2,3} \right]\) . If \(R_1\) is the numerical value of the area of the region bounded by \(y =f (x), x = -2, x = 3\) and the axis of \(x\) and \({R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx\) , thenJEE Mains 2013 Hard
- Let \(\left\{a_{n}\right\}_{n=0}^{\infty}\) be a sequence such that \(a_{0}=a_{1}=0\) and \(a_{ n +2}=3 a_{ n +1}-2 a_{ n }+1, \forall n \geq 0\).Then \(a_{25} a_{23}-2 a_{25} a_{22}-2 a_{23} a_{24}+4 a_{22} a_{24}\) is equal to.JEE Mains 2022 Hard
- The number of solutions of \(\sin ^2 \mathrm{x}+\left(2+2 \mathrm{x}-\mathrm{x}^2\right) \sin \mathrm{x}-3(\mathrm{x}-1)^2=0\), where \(-\pi \leq \mathrm{x} \leq \pi\), is ..........JEE Mains 2024 Hard
- Let a line \(L\) be perpendicular to both the lines \(L_1: \dfrac{x+1}{3} = \dfrac{y+3}{5} = \dfrac{z+5}{7}\) and \(L_2: \dfrac{x-2}{1} = \dfrac{y-4}{4} = \dfrac{z-6}{7}\). If \(\theta\) is the acute angle between the lines \(L\) and \(L_3: \dfrac{x - \dfrac{8}{7}}{2} = \dfrac{y - \dfrac{4}{7}}{1} = \dfrac{z}{2}\), then \(\tan\theta\) is equal to:JEE Mains 2026 Medium
- The value of \(\cot \left( {\sum\limits_{n = 1}^{19} {{{\cot }^{ - 1}}\left( {1 + \sum\limits_{p = 1}^n {2p} } \right)} } \right)\) isJEE Mains 2019 Hard