MCQ
If $\sin\theta=\frac{1}{2}$ then $\cot\theta=?$
- A$\frac{1}{\sqrt3}$
- ✓$\sqrt{3}$
- C$\frac{\sqrt3}{2}$
- D$1$
✓
Answer
Correct option: B.
$\sqrt{3}$
$\sin^2\theta+\cos^2\theta=1$
$\Rightarrow\Big(\frac{1}2{}\Big)^2+\cos^2\theta=1$
$\Rightarrow\cos^2\theta=1-\frac{1}{4}=\frac{3}{4}$
$\Rightarrow\cos\theta=\frac{\sqrt3}{2}$
$\therefore\cot\theta=\frac{\cos\theta}{\sin\theta}$
$=\frac{\frac{\sqrt3}{2}}{\frac{1}{2}}=\sqrt3$
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
The sum of the exponents of the prime factors in the prime factorisation of $196$, is:
→The angle of depression of a car parked on the road from the top of a $150 m$ high tower is $30^{\circ}$. The distance of the car from the tower (in metres) is
→If $a m \neq b l$, then the pair of equations $a x+b y=c, l x+m y=n$
→In the given figure, if $P Q \| B C$. Find $A Q$.
→If $(a^2+ b^2)x^2+ 2(ab + bd)x + c^2+ d^2= 0$ has no real roots, then:
→Mark the correct alternative in the following:
The first three terms of an A.P. respectively are $3y - 1, 3y + 5$ and $5y + 1$. Then, $y$ equals:
→The first three terms of an A.P. respectively are $3y - 1, 3y + 5$ and $5y + 1$. Then, $y$ equals:
The roots of the equation $x^2-2 x-\left(r^2-1\right)=0$ are
→If HCF $(x, y)=1$ then HCF $(x-y, x+y)=$ ................
→If $TP$ and $TQ $are two tangents to a circle with centre $O$ so that $\angle\text{POQ}=110^{\circ},$ then, $\angle\text{PTQ}$ is equal to:
→A card is drawn at random from a well-shuffled deck of $52$ cards. What is the probability of getting a black king?
→