Question

Convert into simplest form: cosec (5π + θ)

Answer 1

=1/5π+θ
=1/sin(4π+(π+θ). = 1/-sinθ
= -cosecθ.

Answer 2

Using Trigonometric Identities of Angles,

$cosec (2\pi + \theta) = cosec\theta$

Given: $Cosec(5\pi+\theta)$

$5\pi+\theta$ can we write as, $4\pi+\pi+\theta$

$cosec (4\pi + (\pi + \theta)) = cosec(\pi + \theta)$

In the third quadrant, the value of the $cosec\theta$ is negative.

$cosec(\pi + \theta)=-cosec\theta$