Find the value of

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

$=-\operatorname{cosec} 30^{\circ}$

$=-2\left[\because \operatorname{cosec} 30^{\circ}=2\right]$