Question:
Find the value of
$\operatorname{cosec}\left(-750^{\circ}\right)$
Solution:
To find: Value of cosec (-750°)
We have,
$\operatorname{cosec}\left(-750^{\circ}\right)=-\operatorname{cosec}\left(750^{\circ}\right)$
${[\because \operatorname{cosec}(-\theta)=-\operatorname{cosec} \theta] }$
$=-\operatorname{cosec}\left[90^{\circ} \times 8+30^{\circ}\right]$
Clearly, $405^{\circ}$ is in $\mathrm{Ist}$ Quadrant and the multiple of $90^{\circ}$ is even
$=-\operatorname{cosec} 30^{\circ}$
$=-2\left[\because \operatorname{cosec} 30^{\circ}=2\right]$