JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
For \(\alpha, \beta \in\left(0, \frac{\pi}{2}\right)\), let \(3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)\) and a real number \(k\) be such that \(\tan \alpha=k \tan \beta\). Then the value of \(\mathrm{k}\) is equal to :
- A \(-\frac{2}{3}\)
- B \(-5\)
- C \(\frac{2}{3}\)
- D \( 5\)
Answer & Solution
Correct Answer
(B) \(-5\)
Step-by-step Solution
Detailed explanation
\(3\sin \alpha \cos \beta+3 \sin \beta \cos \alpha\) \(=2 \sin \alpha \cos \beta-2 \sin \beta \cos \alpha\) \(5 \sin \beta \cos \alpha=-\sin \alpha \cos \beta\) \(\tan \beta=-\frac{1}{5} \tan \alpha \) \(\tan \alpha=-5 \tan \beta\) Not possible as \(\tan \alpha, \tan \beta\) are…
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 the circles \(C_1 : |z| = r\) and \(C_2 : |z - 3 - 4i| = 5\), \(z \in \mathbb{C}\), be such that \(C_2\) lies within \(C_1\). If \(z_1\) moves on \(C_1\), \(z_2\) moves on \(C_2\) and \(\min |z_1 - z_2| = 2\), then \(\max |z_1 - z_2|\) is equal to:JEE Mains 2026 Hard
- If a curve passes through the point \(\left( {2\,,\,\frac{7}{2}} \right)\) and has slope \(\left( {1 - \frac{1}{{{x^2}}}} \right)\) at anypoint \((x, y)\) on it, then the ordinate of the point on the curve whose abscissa is \(- 2\) isJEE Mains 2013 Hard
- If \(z \) is a complex number of unit modulus and argument \(\theta\), then \({\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)\) equals.JEE Mains 2013 Medium
- Let \(B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]\) and \(A\) be a \(2 \times 2\) matrix such that \(\mathrm{AB}^{-1}=\mathrm{A}^{-1}\). If \(\mathrm{BCB}^{-1}=\mathrm{A}\) and \(\mathrm{C}^4+\alpha \mathrm{C}^2+\beta \mathrm{I}=\mathrm{O}\), then \(2 \beta-\alpha\) is equal to :JEE Mains 2024 Hard
- If the tangent to the curve, \(y = x^3 + ax -b\) at the point \((1, -5)\) is perpendicular to the line, \(-\,x + y + 4 = 0,\) then which one of the following, points lies on the curveJEE Mains 2019 Hard
- If all the six digit numbers \(x_1 x_2 x_3 x_4 x_5 x_6\) with \(0 < x_1 < x_2 < x_3 < x_4 < x_5 < x_6\) are arranged in the increasing order, then the sum of the digits in the \(72^{\text {th }}\) number is \(............\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(f(x)=\frac{1}{7-\sin 5 x}\) be a function defined on \(R\). Then the range of the function \(f(x)\) is equal to:JEE Mains 2024 Medium
- Let \(S=\left\{ x : x \in R \text { and }(\sqrt{3}+\sqrt{2})^{ x ^2-4}+(\sqrt{3}-\sqrt{2})^{ x ^2-4}=10\right\} \text {. }\) Then \(n ( S )\) is equal toJEE Mains 2023 Hard
- Bag \(B_1\) contains 6 white and 4 blue balls, Bag \(B_2\) contains 4 white and 6 blue balls, and Bag \(B_3\) contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag \(B_2\), is :JEE Mains 2025 Easy
- The area enclosed between the curves \(y=x|x|\) and \(\mathrm{y}=\mathrm{x}-|\mathrm{x}|\) is :JEE Mains 2024 Medium
- The sum of all possible values of \( n \in N \) so that the coefficients of \(x\), \( x^{2} \) and \( x^{3} \) in the expansion of \( (1+x^{2})^{2}(1+x)^{n} \) are in arithmetic progression is :JEE Mains 2026 Easy
- If the plane \(2x -y + 2z + 3 = 0\) has the distances \(\frac {1}{3}\) and \(\frac {2}{3}\) units from the planes \(4x -2y + 4z + \lambda = 0\) and \(2x -y + 2z + \mu = 0,\) respectively, then the maximum value of \(\lambda + \mu \) us equal toJEE Mains 2019 Hard