How do you verify #csctheta-cottheta=1/(csctheta+cottheta)#?

Question

1675 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-12T10:56:52

see below

#csctheta-cot theta=1/(csctheta+cot theta)#

Right Side:#=1/(csctheta+cot theta)#

#=1/(csctheta+cot theta)*(csctheta-cot theta)/(csctheta-cot theta)#

#=(csctheta-cot theta)/(csc^2theta-cot ^2theta)#

#=(csctheta-cot theta)/1# Note: #csc^2theta-cot ^2theta=1# from the

pythagorean identity #1+cot^2theta=csc^2theta#

#=csctheta-cot theta#

#:.=# Left Side