JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of elements in the set \(S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^6 \theta+2=0\right\}\) is \(...........\).
- A \(10\)
- B \(8\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
Sol. \(3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^6 \theta+2=0\) \(\Rightarrow \quad 3 \cos ^4 \theta-3 \cos ^2 \theta-2 \cos ^2 \theta-2 \sin ^6 \theta+2=0\) \(\Rightarrow \quad 3 \cos ^4 \theta-3 \cos ^2 \theta+2 \sin ^2 \theta-2 \sin ^6 \theta=0\)…
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 two lines \(L_1\) and \(L_2\) in space, are defined by \({L_1} = \{ x = \sqrt \lambda y + \left( {\sqrt \lambda - 1} \right),z = \left( {\sqrt \lambda - 1} \right)y + \sqrt \lambda \} \) and \({L_2} = \{ x = \sqrt \mu y + \left( {1 - \sqrt \mu } \right),z = \left( {1 - \sqrt \mu } \right)y + \sqrt \mu \} \) then \(L_1\) is perpendicular to \(L_2\), for all non-negative reals \(\lambda \) and \( \mu \), such thatJEE Mains 2013 Hard
- In the expansion of \(\left(9x-\dfrac{1}{3\sqrt{x}}\right)^{18}\), \(x>0\), if the term independent of \(x\) is \((221)k\), then \(k\) is equal to:JEE Mains 2026 Medium
- The sum of all those terms, of the anithmetic progression \(3,8,13, \ldots \ldots .373\), which are not divisible by \(3\),is equal to \(.......\).JEE Mains 2023 Hard
- Let \(|\vec{a}|=2,|\vec{b}|=3\) and the angle between the vectors \(\vec{a}\) and \(\vec{b}\) be \(\frac{\pi}{4}\). Then \(|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^2\) is equal toJEE Mains 2023 Medium
- Let \(f(x)=x^{6}+2 x^{4}+x^{3}+2 x+3, x \in R\). Then the natural number \(\mathrm{n}\) for which \(\lim _{x \rightarrow 1} \frac{\mathrm{x}^{\mathrm{n}} \mathrm{f}(1)-\mathrm{f}(\mathrm{x})}{\mathrm{x}-1}=44\) is ...... .JEE Mains 2021 Hard
- If the sum of the coefficients of \(x^7\) and \(x^{14}\) in the expansion of \(\left(\dfrac{1}{x^3} - x^4\right)^n\), \(x \neq 0\), is zero, then the value of \(n\) is __________.JEE Mains 2026 Hard
More PYQs from JEE Mains
- If the function \(f(x)\, = \left\{ {\begin{array}{*{20}{c}}{ - x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x < 1\,\,\,\,}\\{a + {{\cos }^{ - 1}}(x + b),\,\,\,\,\,\,\,\,\,1 \le x \le 2} \end{array}} \right.\) is differentiable at \(x = 1 ,\) then \(\frac {a}{b}\) is equal toJEE Mains 2016 Hard
- If the probability that the random variable X takes the value \(x\) is given by \(P(X=x)=k(x+1) 3^{-x}\), \(\mathrm{x}=0,1,2,3 \ldots \ldots\), where k is a constant, then \(\mathrm{P}(\mathrm{X} \geq 3)\) is equal toJEE Mains 2025 Medium
- Let a differentiable function \(f\) satisfy \(f ( x )+\int \limits_3^{ x } \frac{ f ( t )}{ t } dt =\sqrt{ x +1}, x \geq 3\). Then \(12 f (8)\) is equal to:JEE Mains 2023 Hard
- If the system of linear equations \(x - 2y + kz = 1\) ; \(2x + y + z = 2\) ; \(3x - y - kz = 3\) Has a solution \((x, y, z) \ne 0\), then \((x, y)\) lies on the straight line whose equation isJEE Mains 2019 Hard
- If \(f(x)=\frac{2^{2 x}}{2^{2 x}+2}, x \in R\) then \(f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\ldots \ldots . .+f\left(\frac{2022}{2023}\right)\) is equal toJEE Mains 2023 Hard
- If \(\alpha, \beta\) are the roots of the equation, \(x^2-x-1=0\) and \(S_n=2023 \alpha^n+2024 \beta^n\), thenJEE Mains 2024 Hard