JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(\cos \,\alpha + \cos \,\beta = \frac{3}{2}\) and \(\sin \,\alpha + \sin \,\beta = \frac{1}{2}\) and \(\theta \) is the the arithmetic mean of \(\alpha \) and \(\beta \) , then \(\sin \,2\theta + \cos \,2\theta \) is equal to
- A \(\frac{3}{5}\)
- B \(\frac{7}{5}\)
- C \(\frac{4}{5}\)
- D \(\frac{8}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{5}\)
Step-by-step Solution
Detailed explanation
Let \(\cos \alpha+\cos \beta=\frac{3}{2}\) \(\Rightarrow 2 \cos \frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}=\frac{3}{2}\) ..... \((i)\) and \(\sin \alpha+\sin \beta=\frac{1}{2}\) \(\Rightarrow 2 \sin \frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}=\frac{1}{2}\) .....…
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 \(S=\left\{z \in C :\left|\frac{z-6 i}{z-2 i}\right|=1\right.\) and \(\left.\left|\frac{z-8+2 i}{z+2 i}\right|=\frac{3}{5}\right\}\). Then \(\sum_{z \in s}|z|^2\) is equal toJEE Mains 2026 Medium
- The set of values of \(k\) for which the circle \(C : 4 x^{2}+4 y^{2}-12 x+8 y+k=0\) lies inside the fourth quadrant and the point \(\left(1,-\frac{1}{3}\right)\) lies on or inside the circle \(C\) isJEE Mains 2022 Hard
- Let \(f\) be a differentiable function satisfying
\(f(x)=1-2x+\int_{0}^{x}e^{(x-t)}f(t)dt, x\in R\) and let
\(g(x)=\int_{0}^{x}(f(t)+2)^{15}(t-4)^{6}(t+12)^{17}dt, x\in R.\)
If p and q are respectively the points of local minima and local maxima of g, then the value of \(|p+q|\) is equal to ___ .JEE Mains 2026 Easy - If \(\left(\frac{3^{6}}{4^{4}}\right) \mathrm{k}\) is the term, independent of \(\mathrm{x}\), in the binomial expansion of \(\left(\frac{\mathrm{x}}{4}-\frac{12}{\mathrm{x}^{2}}\right)^{12}\), then \(\mathrm{k}\) is equal to ...... .JEE Mains 2021 Medium
- The number of solutions of the equation \(x +2 \tan x =\frac{\pi}{2}\) in the interval \([0,2 \pi]\) is :JEE Mains 2021 Hard
- If tangents are drawn to the ellipse \(x^2 + 2y^2 = 2\) at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curveJEE Mains 2019 Hard
More PYQs from JEE Mains
- If \(1, \log _{10}\left(4^{x}-2\right)\) and \(\log _{10}\left(4^{x}+\frac{18}{5}\right)\) are in
arithmetic progression for a real number \(x\) then the value of the determinant \(\left|\begin{array}{ccc}2\left(x-\frac{1}{2}\right) & x-1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0\end{array}\right|\) is equal to ...... .JEE Mains 2021 Hard - If \(z = \frac{{\sqrt 3 }}{2} + \frac{i}{2}\,\,\,\left( {i = \sqrt { - 1} } \right)\), then \({\left( {1 + iz + {z^5} + i{z^8}} \right)^9}\) is equal toJEE Mains 2019 Hard
- Let \(\alpha\) and \(\beta\) be two real roots of the equation \((\mathrm{k}+1) \tan ^{2} \mathrm{x}-\sqrt{2} \cdot \lambda \tan \mathrm{x}=(1-\mathrm{k})\) where \(\mathrm{k}(\neq-1)\) and \(\lambda\) are real numbers. If \(\tan ^{2}(\alpha+\beta)=50,\) then a value of \(\lambda\) is :JEE Mains 2020 Hard
- A possible value of \(^{\prime}x^{\prime}\), for which the ninth term in the expansion of \(\left\{3^{\log _{3} \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\right\}^{10}\) in the increasing powers of \(3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\) is equal to \(180\) , is:JEE Mains 2021 Hard
- The integral \(\int\limits_{7\pi /4}^{7\pi /3} {\sqrt {{{\tan }^2}\,x}\,dx } \) is equal toJEE Mains 2013 Hard
- 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