Question

If $\theta$ is any acute angle, what is the area of a square with adjacent sides $sin\theta$ and $cosec\theta$?

• A. $sin\theta \times cos\theta$
• B. $co{s}^2\theta$
• C. $si{n}^2\theta$

Answer 1

In a square, lengths of all the sides are equal.

Which means $sin\theta =cosec\theta$.

$sin\theta =cosec\theta \text{only when}\theta ={90}^0$

$\therefore$ $\theta ={90}^{\circ }$
$\Rightarrow$ length of side = $sin{90}^{\circ }=1$
So, area = 1 $\times$ 1
= 1