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.

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