Prove the following identity
cosec (theta) + tan (theta) = 1 / [cosec (theta) - tan (theta)]
cosec (theta) + tan (theta)
= 1 / sin (theta) + (sin (theta)/cos (theta))
= [cos (theta) + sin ^2 (theta) ] / sin (theta) cos (theta)
I require help for further steps
If I substitute sin^2 (theta) = 1 - cos^2 (theta)
then:
= [cos (theta) + 1 - cos^2 (theta) ] / sin (theta) cos (theta)
With the above expression I am unable to prove the identity.
This is where I'm stuck.