# Find the value of $cosec(-1410^{\large\circ})$

$\begin{array}{1 1}(A)\;3&(B)\;4\\(C)\;2&(D)\;5\end{array}$

Toolbox:
• $cosec(2n\pi-\theta)=-cosec\theta$
• $cosec 30^{\large\circ}=2$
$cosec(-1410^{\large\circ})=-cosec 1410^{\large\circ}$
$\Rightarrow -cosec (4\times 360^{\large\circ}-30^{\large\circ})$
$\Rightarrow cosec 30^{\large\circ}$
Since $cosec(2n\pi-\theta)=-cosec \theta$
$cosec 30^{\large\circ}\Rightarrow 2$
Hence $cosec (-1410^{\large\circ})=2$
Hence (C) is the correct answer.