How do you verify the identity $(csctheta-cottheta)^2=(1-costheta)/(1+costheta)$ ?

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Answer 1 · 2016-08-21T08:03:24

the identity is verified

Since $csctheta=1/sintheta and cottheta=costheta/(sintheta)$ ,

you can substitute and have:

$(csctheta-cottheta)^2=(1/sintheta-costheta/(sintheta))^2$

$=((1-costheta)/(sintheta))^2=(1-costheta)^2/(sin^2theta)$

Since $sin^2theta=1-cos^2theta$ , the expression becomes:

$=(1-costheta)^2/(1-cos^2theta)=(1-costheta)^cancel2/(cancel((1-costheta))(1+costheta))=(1-costheta)/(1+costheta)$

and the identity is verified

How do you verify the identity (csctheta-cottheta)^2=(1-costheta)/(1+costheta)(csctheta-cottheta)^2=(1-costheta)/(1+costheta)?