If A = 3 4 , then 32 A 2 5 2 A = - Vidyadip

MCQ

If $\cos A = \frac{3}{4}$, then $32\sin \frac{A}{2}\cos \frac{5}{2}A = $

A
$\sqrt 7 $
✓
$ - \sqrt 7 $
C
$7$
D
$-7$

✓

Answer

Correct option: B.

$ - \sqrt 7 $

b
(b) $\cos A = \frac{3}{4} \Rightarrow \sin A = \frac{{\sqrt 7 }}{4}$

$L.H.S.$ $ = 16(\sin 3A - \sin 2A)$

$ = 16\sin A(3 - 4{\sin ^2}A - 2\cos A)$

$ = 16.\frac{{\sqrt 7 }}{4}\left( {3 - 4.\frac{7}{{16}} - 2.\frac{3}{4}} \right) = - \sqrt 7 $.

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 "M.C.Q (1 Marks)" from STD 11 - 3. trignometrical ratios,functions and identities→STD 11 - 3. trignometrical ratios,functions and identities — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If line joining $(1, 2)$ and $(5, 7)$ is parallel to line joining $(3, 4)$ and $(11, x):$

The remainder when $19^{200}+23^{200}$ is divided by $49$ , is $.........$.

Number of odd numbers of five distinct digits can be formed by the digits $0, 1, 2, 3, 4,$ is:

If $V$ and $S$ are respectively the vertex and focus of the parabola $y^2 + 6y + 2x + 5 = 0,$ then $SV =$

In a triangle, the side lengths are $a = 5, b = 3$ and $c = 2.$ Find the length of the median drawn to the side $c:$

What is the sample space for choosing an odd number from $2$ to $10$ at random?

In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to $30$ . In order to maximise the area of the trapezium, the smallest angle should be

Set $\{x: x \in N, x$ is prime, $3 < x < 5\}$ is :

The number of $4$-digit integers in the closed interval [$2022, 4482$] formed by using the digits $0,2,3,4,6,7$ is. . . . .

The eccentricity of the hyperbola ${x^2} - {y^2} = 25$ is