Verify the identity

Question

cot2 beta/1+csc beta=1-sin beta/sin beta.

Answer 1

did you mean
cot^2 ß/(1+cscß) = (1-sinß)/sinß ?

from the identity
sin^ Ø + cos^2 Ø = 1
if we divide each term by sin^2Ø ......
1 + cot^2 Ø = csc^2 Ø ----> cot^2 Ø = csc^2Ø - 1

LS
= (csc^2 ß - 1)/(1 + csc ß)
= (cscß + 1)(cscß - 1)/(1 + cscß)
= cscß - 1
= 1/sinß - sinß/sinß
= (1 - sinß)/sinß
= RS