Question

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

Answer 1

Please see below.

Explanation:

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)`