Question #14cad

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Answer 1 · 2018-02-13T22:21:38

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