How do you verify the identity $csc2theta=csctheta/(2costheta)$ ?

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Answer 1 · 2017-01-06T07:47:04

Please see below.

As $cscA=1/sinA$ or $sinA=1/cscA$ , we have

$csc2theta=1/(sin2theta)$

But $sin2theta=2sinthetacostheta$

Hence $csc2theta=1/(sin2theta)=1/(2sinthetacostheta)$

= $1/(2xx(1/csctheta)xxcostheta)$

= $csctheta/(2sintheta)$

How do you verify the identity csc2theta=csctheta/(2costheta)csc2theta=csctheta/(2costheta)?