MCQ
If $2 \sin 2 \theta=\sqrt{3}$, then $\theta=$
- ✓$30^{\circ}$
- B$45^{\circ}$
- C$60^{\circ}$
- DNane of these
✓
Answer
Correct option: A.
$30^{\circ}$
(a) : We have, $2 \sin 2 \theta=\sqrt{3}$
$\Rightarrow \sin 2 \theta=\frac{\sqrt{3}}{2} \Rightarrow 20=60^{\circ}$
$
\left[\because \sin 60^{ n }=\frac{\sqrt{3}}{2}\right]
$
$\Rightarrow \theta=\frac{60^{\circ}}{2}=30^{\circ}$
$\Rightarrow \sin 2 \theta=\frac{\sqrt{3}}{2} \Rightarrow 20=60^{\circ}$
$
\left[\because \sin 60^{ n }=\frac{\sqrt{3}}{2}\right]
$
$\Rightarrow \theta=\frac{60^{\circ}}{2}=30^{\circ}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
On increasing the radii of the base and the height of a cone by $20\%$, its volume will increase by:
→$\frac{\cos38^\circ\text{cosec}52^\circ}{\tan18^\circ\tan35^\circ\tan60^\circ\tan72^\circ\tan55^\circ}=?$
→Two circles touch each other externally at $P. AB$ is a common tangent to the circles touching them at $A$ and $B$. The value of $\angle\text{APB}$ is :
→If $p$ and $q$ are two distinct prime numbers, then their HCF is
→In the given figure, a circle touches the side DF of $\triangle\text{EDF}$ at H and touches ED and EF produced at K and M respectively. If EK = 9cm then the perimeter of $\triangle\text{EDF}$ is:
→If in a $ \triangle\text{ABC}, \angle\text{C}=90^\circ$ and $\angle\text{B}=45^\circ,$ then state which of the following is true?
→If $\text{x}=\text{r}\sin\theta\cos\phi,\text{y}=\text{r}\sin\phi$ and ${z}=\text{r}\cos\theta,$ then:
→A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option :
Assertion (A) : If one root of the quadratic equation $4 x^2-10 x+(k-4)=0$ is reciprocal of the other, then value of k is 8 .
Reason $( R )$ : Roots of the quadratic equation $x ^2- x +1=0$ are real.
→Assertion (A) : If one root of the quadratic equation $4 x^2-10 x+(k-4)=0$ is reciprocal of the other, then value of k is 8 .
Reason $( R )$ : Roots of the quadratic equation $x ^2- x +1=0$ are real.
If a pair of linear equations is consistent then their graph lines will be
If three coins are tossed simultaneously, then the probability of getting at least two heads, is