Question

Which of the following is true if $0°\le \theta <90°?$

• A. $0<\frac{1}{cosec\theta }\le 1$
• B. $0<\frac{1}{cosec\theta }<1$
• C. $0\le \frac{1}{cosec\theta }<1$
• D. $0\le \frac{1}{cosec\theta }\le 1$

Answer 1

The correct option is C $0\le \frac{1}{cosec\theta }<1$

$\text{Given,}0°\le \theta <90°$

$\Rightarrow sin0°\le sin\theta <sin90°$
$\Rightarrow 0\le sin\theta <1$
$\Rightarrow 0\le \frac{1}{cosec\theta }<1(\text{As,}sin\theta =\frac{1}{cosec\theta })$