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

More "MCQ" from 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The sum of the solutions of the equation $\left| {\sqrt x - 2} \right| + \sqrt x \left( {\sqrt x - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

What is the distance between the points (2, -1, 3) and (-2, 1, 3):

The least positive integer n such that $\Big(\frac{2\text{i}}{1+\text{i}}\Big)^\text{n}$ is a positive integer, is:

$P(3,1),\;Q(6,5)$ and $R(x,y)$ are three points such that the angle $PRQ$ is a right angle and the area of the $\Delta RPQ=5$, then the number of such points $R$ is

How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$ ?

A circle touches the y-axis at the point $(0, 4)$ and cuts the $x$ - axis in a chord of length $6$ units. The radius of the circle is

Line $Ax + By + C = 0$ cuts circle ${x^2} + {y^2} + ax + by + c = 0$ in $P$ and $Q$ and the line $A'x + B'y + C' = 0$ cuts the circle ${x^2} + {y^2} + a'x + b'y + c' = 0$ in $R$ and $S$. If the four points $P, Q, R$ and $S$ are con-cyclic, then $D = \left| {\begin{array}{*{20}{c}}{a - a'}&{b - b'}&{c - c'}\\A&B&C\\{A'}&{B'}&{C'}\end{array}} \right|$ =

Let the sum of the first $n$ terms of a non-constant $A.P., a_1, a_2, a_3, ……$ be $50\,n\, + \,\frac{{n\,(n\, - 7)}}{2}A,$ where $A$ is a constant. If $d$ is the common difference of this $A.P.,$ then the ordered pair $(d,a_{50})$ is equal to

The value of $9^{\frac13}.9^{\frac19}.9^{\frac{1}{27}}\dots\text{to }\infty,$ is:

The equation ${\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0$ is solvable for