JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,\) the number of solutions of the given equation when \(x \in\left[0, \frac{\pi}{2}\right]\) is
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\sqrt{3}(\cos x)^{2}-\sqrt{3} \cos x+\cos x-1=0\) \(\Rightarrow(\sqrt{3} \cos x+1)(\cos x-1)=0\) \(\Rightarrow \cos x=1\) or \(\cos x=-\frac{1}{\sqrt{3}}\) (reject) \(\Rightarrow x=0\) only
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 number of bijective functions \(f :\{1,3,5, 7, \ldots \ldots . .99\} \rightarrow\{2,4,6,8, \ldots \ldots, 100\}\), such that \(f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \ldots f(99), \quad\) isJEE Mains 2022 Hard
- If for \(p \neq q \neq 0\), then function,\(f(x)=\frac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+q x}-9}\)is continuous at \(x=0\), thenJEE Mains 2022 Hard
- The probability that a randomly chosen \(5-digit\) number is made from exactly two digits isJEE Mains 2020 Hard
- Let \(\hat{a}\) and \(\hat{b}\) be two unit vectors such that the angle between them is \(\frac{\pi}{4}\). If \(\theta\) is the angle between the vectors \((\hat{a}+\hat{b})\) and \((\hat{a}+2 \hat{b}+2(\hat{a} \times \hat{b}))\) then the value of \(164 \cos ^{2} \theta\) is equal to.JEE Mains 2022 Hard
- Let \(a, b \in R, a \neq 0\) be such that the equation, \(a x^{2}-2 b x+5=0\) has a repeated root \(\alpha,\) which is also a root of the equation, \(x^{2}-2 b x-10=0\) If \(\beta\) is the other root of this equation, then \(\alpha^{2}+\beta^{2}\) is equal toJEE Mains 2020 Hard
- If \(y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x\), then \(96 y^{\prime}\left(\frac{\pi}{6}\right)\) is equal to :JEE Mains 2024 Hard
More PYQs from JEE Mains
- The point represented by \(2 + i\) in the Argand plane moves \(1\,unit\) eastwards, then \(2\,units\) northwards and finally from there \(2\sqrt 2\,units\) in the south-westwards direction. Then its new position in the Argand plane is at the point represented byJEE Mains 2016 Hard
- Let \(a, b, c, d\) and \(p\) be any non zero distinct real numbers such that \(\left(a^{2}+b^{2}+c^{2}\right) p^{2}-2(a b+b c+ cd ) p +\left( b ^{2}+ c ^{2}+ d ^{2}\right)=0 .\) ThenJEE Mains 2020 Hard
- A bag contains 10 balls out of which k are red and \((10-k)\) are black, where \(0\le k\le10.\) If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:JEE Mains 2026 Easy
- A line \('l'\) passing through origin is perpendicular to the lines \(l_{1}: \overrightarrow{ r }=(3+ t ) \hat{ i }+(-1+2 t ) \hat{ j }+(4+2 t ) \hat{ k }\) ; \(l_{2}: \overrightarrow{ r }=(3+2 s ) \hat{ i }+(3+2 s ) \hat{ j }+(2+ s ) \hat{ k }\) . If the co-ordinates of the point in the first octant on \({ }^{\prime} l_{2}^{\prime}\) at a distance of \(\sqrt{17}\) from the point of intersection of \(^{\prime} l^{\prime}\) and \({ }^{\prime} l_{1}^{\prime}\) are \(( a , b , c ),\) then \(18( a+ b + c )\) is equal to ........ .JEE Mains 2021 Hard
- Let there be three independent events \(E _{1}, E _{2}\) and \(E _{3}\). The probability that only \(E _{1}\) occurs is \(\alpha\), only \(E _{2}\) occurs is \(\beta\) and only \(E _{3}\) occurs is \(\gamma .\) Let \('p'\) denote the probability of none of events occurs that satisfies the equations \((\alpha-2 \beta) p =\alpha \beta\) and \((\beta-3 \gamma) p =2 \beta \gamma .\) All the given probabilities are assumed to lie in the interval \((0,1)\) Then, \(\frac{\text { Probability of occurrence of } E _{1}}{\text { Probability of occurrence of } E _{3}}\) is equal to ..........JEE Mains 2021 Hard
- The value of \(\int_{-1}^{1} x ^{2} e ^{\left[x^{3}\right]} dx ,\) where \([ t ]\) denotes the greatest integer \(\leq t ,\) isJEE Mains 2021 Hard