2 , ^2 + 4 , , ,( + ) , , , , , + ,2 ,( + ) = - Vidyadip

MCQ

$2\,{\sin ^2}\beta + 4\,\,\cos \,(\alpha + \beta )\,\,\sin \,\alpha \,\sin \,\beta + \cos \,2\,(\alpha + \beta ) = $

A
$\sin \,\,2\alpha $
B
$\cos \,\,2\beta $
✓
$\cos \,\,2\alpha $
D
$\sin \,\,2\beta $

✓

Answer

Correct option: C.

$\cos \,\,2\alpha $

c
(c) $\cos 2(\alpha + \beta ) = 2{\cos ^2}(\alpha + \beta ) - 1,$

$2{\sin ^2}\beta = 1 - \cos 2\beta $

$L.H.S.$ $ = - \cos 2\beta + 2\cos (\alpha + \beta )\,[2\sin \alpha \sin \beta + \cos (\alpha + \beta )]$

$ = - \cos 2\beta + 2\cos (\alpha + \beta )\cos (\alpha - \beta )$

$ = - \cos 2\beta + (\cos 2\alpha + \cos 2\beta ) = \cos 2\alpha $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

For the two positive numbers $a , b$, if $a , b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{ a }, 10$ and $\frac{1}{ b }$ are in an arithmetic progression, then, $16 a+12 b$ is equal to $.........$.

If $M = \left[ {\begin{array}{*{20}{c}}1&2\\2&3\end{array}} \right]$ and ${M^2} - \lambda M - {I_2} = 0$, then $\lambda = $

If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then The function $ f (x)$

The equation to the orthogonal trajectories of the system of parabolas $y = ax^2$ is

Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then, the coefficient of $x$ in $f(x)$ is

Let $A = \left\{ {\left( {x,y} \right):{y^2} \le 4x,y - 2x \ge - 4} \right\}$ .The area of the region $A$ is

The area (in sq. units) of the region bounded by the parabola, $y = x^2 + 2$ and the lines, $y = x + 1, x = 0$ and $x = 3$, is

A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red

Let $\quad f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|$, $x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right]$. If $\alpha$ and $ \beta$ respectively are the maximum and the minimum values of $f$, then