What is #(3cottheta)/5# in terms of #sectheta#?

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Answer 1 · 2016-04-15T01:27:04

#3/5*cot theta=3/5*sqrt(sec^2 theta-1)/(sec^2 theta-1)#

the given expression is

#3/5*cot theta#

#tan^2 theta+1=sec^2 theta#

#tan^2 theta=sec^2 theta-1#

#cot^2 theta=1/tan^2 theta#

#cot^2 theta=1/(sec^2 theta-1)#

#cot theta=sqrt(1/(sec^2 theta-1))=1/sqrt(sec^2 theta-1)=sqrt(sec^2 theta-1)/(sec^2 theta-1)#

Therefore

#3/5*cot theta=3/5*sqrt(sec^2 theta-1)/(sec^2 theta-1)#

God bless....I hope the explanation is useful.