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  4. The value of operatornamecosec(-1410)° is equal to

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Q. The value of $\operatorname{cosec}(-1410)^{\circ}$ is equal to

Trigonometric Functions

Solution:

Since, we know that
$\operatorname{cosec}(-\theta) =-\operatorname{cosec} \theta$
$\therefore \operatorname{cosec}\left(-1410^{\circ}\right)$
$ =-\operatorname{cosec}(360 \times 4-30)^{\circ}$
$ =-\left(-\operatorname{cosec} 30^{\circ}\right)$
$=\operatorname{cosec} 30^{\circ} $
$ {[\because \operatorname{cosec}(2 n \pi-\theta)=-\operatorname{cosec} \theta] }$
$ =2$