Given #7 cosec theta -3cot theta =7#
To prove #3cosec theta - 7cot theta = 3#
Now
#(3cosec theta - 7cot theta)^2#
#=9csc^2theta+49cot^2theta-2*3csctheta*7cottheta#
#=9+9cot^2theta+49csc^2theta-49-2*3csctheta*7cottheta#
#=(3cottheta)^2+(7csctheta)^2-2*3cottheta*7csctheta-40#
#=>(7csctheta-3cottheta)^2-40#
#=>7^2-40=9=3^2#
So
#3cosec theta - 7cot theta=3#
Proved