If ^2 x-2 x+1 4 =0, then x has value - Vidyadip

MCQ

If $\sin ^2 x-2 \cos x+\frac{1}{4}=0$, then $x$ has value

A
$2 n \pi+\frac{\pi}{4}$
✓
$2 n \pi \pm \frac{\pi}{3}$
C
$2 n \pi+\frac{\pi}{6}$
D
$2 n \pi+\frac{\pi}{12}$

✓

Answer

Correct option: B.

$2 n \pi \pm \frac{\pi}{3}$

(B) $\sin ^2 x-2 \cos x+\frac{1}{4}=0$
$\Rightarrow 1-\cos ^2 x-2 \cos x+\frac{1}{4}=0$
Putting $\cos x= t$, we get
$1-t^2-2 t+\frac{1}{4}=0 \Rightarrow 4 t^2+8 t-5=0$
$\therefore \quad t =\frac{1}{2}$ or $t =-\frac{5}{2}$
Since, $\cos x \neq \frac{-5}{2}$
$\therefore \cos x=\frac{1}{2}=\cos \frac{\pi}{3} \Rightarrow x=2 n \pi \pm \frac{\pi}{3}$

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 Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The distance of the point $2 \hat{i}+\hat{j}+\hat{k}$ from the line $\bar{r}=-\hat{i}+2 \hat{j}+2 \hat{k}+\lambda(3 \hat{i}+\hat{k})$ is

If the pair of lines $6 x^2+x y-y^2=0$ and $3 x^2- a x y-y^2=0, a >0$ have a common line, then $a =$

In $a \triangle A B C$, if $2 s=a+b+c$ and $( s - b )( s - c )=x \sin ^2 \frac{A}{2}$, then $x=$

If $2 \cos ^2 x+3 \sin x-3=0,0 \leq x \leq 180^{\circ}$, then $x=$

If the foot of the perpendicular drawn from the origin to the plane is $(4, −2, -5),$ then the equation of the plane is ______

If $\text{A}=\begin{bmatrix}2&-1&3\\-4&5&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&3\\4&-2\\1&5\end{bmatrix},$ then:

The angle of intersection of the parabolas $y^2 = 4 ax$ and $x^2 = 4ay$ at the origin is:

The angle between the line $\frac{x+1}{3}=\frac{y-1}{2}=\frac{z-2}{4}$ and the plane $2 x+y-3 z+4=0$ is

$\int\limits^\text{e}_1\log\text{x}\text{ dx}=$

If the sum of the squares of the distance of a point from the three co-ordinate axes be 36 , then its distance from the origin is