Question

$\mathrm{A}=\mathrm{cosec}2°$ and $B=\cos ec2$, Then which of the following holds true $?$

• A. $A>B$
• B. $A<B$
• C. $A=B$
• D. $A=2B$

Answer 1

The correct option is A

$A>B$

Calculating the value of both $A$and $B$:

$B=\cos ec2$

Here, $2$ is in radian, so converting it into degree.

We know that, to convert the radian into degree we multiply it by $\frac{180}{\mathrm{\pi }}$

$$\begin{gathered} \therefore 2\mathrm{radian}=2\times \frac{180}{\mathrm{\pi }} \\ 2\mathrm{radian}=2\times \frac{180}{22}\times 7 \\ 2\mathrm{radian}=114.59° \end{gathered}$$

So,

$$\begin{gathered} \mathrm{B}=\mathrm{cosec}114.59\cong \mathrm{cosec}115° \\ \mathrm{B}=\mathrm{cosec}115° \end{gathered}$$

Now,

$$\begin{gathered} \mathrm{B}=\mathrm{cosec}115° \\ \mathrm{B}=\mathrm{cosec}\left(180°-65°\right) \\ \mathrm{B}=\mathrm{cosec}65° \end{gathered}$$

Now, we know that the value of $\sin \mathrm{\theta }$ increases from $0°to90°$.

So, we can say that $\sin 2°<\sin 65°$

The value of cosec will be $\mathrm{cosec}2°>\mathrm{cosec}65°$

Therefore, $A>B$

Hence, option A is correct..