If =-3 5 , where < <3 2 , then ( 2 )= - Vidyadip

MCQ

If $\sin \alpha=\frac{-3}{5}$, where $\pi<\alpha<\frac{3 \pi}{2}$, then $\cos \left(\frac{\alpha}{2}\right)=$

✓
$\frac{-1}{\sqrt{10}}$
B
$\frac{1}{\sqrt{10}}$
C
$\frac{3}{\sqrt{10}}$
D
$\frac{-3}{\sqrt{10}}$

✓

Answer

Correct option: A.

$\frac{-1}{\sqrt{10}}$

(A)
$\cos \left(\frac{\alpha}{2}\right)=-\sqrt{\frac{1+\cos \alpha}{2}}$
$\ldots\left[\because \pi<\alpha<\frac{3 \pi}{2} \Rightarrow \frac{\pi}{2}<\frac{\alpha}{2}<\frac{3 \pi}{4}\right]$
Now, $\cos \alpha=-\sqrt{1-\sin ^2 \alpha}$\[\ldots\left[\because \pi<\alpha<\frac{3 \pi}{2}\right]\]
$=-\sqrt{1-\frac{9}{25}}=-\frac{4}{5}$
$\therefore \quad \cos \frac{\alpha}{2}=-\sqrt{\frac{1-\frac{4}{5}}{2}}=-\frac{1}{\sqrt{10}}$

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 Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $f(x)$ is continuous in $[0, \pi]$, where
$f(x)=\left\{\begin{array}{ll}x+a \sqrt{2} \sin x, & 0 \leq x < \frac{\pi}{4} \\2 x \cot x+b, & \frac{\pi}{4} \leq x \leq \frac{\pi}{2}, \text { then } \\a \cos 2 x-b \sin x, & \frac{\pi}{2} < x \leq \pi\end{array}\right.$

If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles $x^2+y^2+2 x-4 y-20=0$ and $x^2+y^2-4 x+2 y-44=0$ is $ 2: 3 $, then the locus of Pis a circle with centre

$\lim _{x \rightarrow 0} \frac{4^x-9^x}{x\left(4^x+9^x\right)}=$

If $A =133^{\circ}$, then $2 \cos \frac{A}{2}$ is equal to

The length of perpendicular drawn from origin on the line joining ( $x^{\prime}, y^{\prime}$ ) and ( $x^{\prime \prime}, y^{\prime \prime}$ ), is

$\lim _{x \rightarrow 1} \frac{x^8-2 x+1}{x^4-2 x+1}$ equals

If $k=\sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18}$, then the numerical value of $k$ is

If $2 x=-1+\sqrt{3} i$, then the value of $\left(1-x^2+x\right)^6-\left(1-x+x^2\right)^6$ is

If $p(n): 2n < (1 \times 2 \times 3 \times ... \times n).$ Then the smallest positive integer for which $p(n)$ is true is:

If the eccentricities of the hyperbolas $\frac{x^2}{ a ^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{b^2}-\frac{x^2}{ a ^2}=1$ be e and $e_1$, then $\frac{1}{e^2}+\frac{1}{e^2}=$