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

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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

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