Question

$a=\text{cosec}{2}^0,b=\text{c}osec2$ , 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 B $a>b$

$a=\text{cosec}{2}^{o}b=\text{cosec}\frac{2\ast {180}^o}{\pi }=\text{cosec}{114.59}^o\approx \text{cosec}{115}^o=\text{cosec}(180-65{)}^o=\text{cosec}{65}^o$

Now,
$2^o<{65}^o$
$\Rightarrow \sin 2^o<\sin {65}^o$
$\Rightarrow \text{cosec}{2}^o>\text{cosec}{65}^o$
$\therefore \text{cosec}{2}^o>\text{cosec}{2}^c$

Therefore, Answer is $a>b$