Csc(x) - cot(x) forms an identity with which of the following?
1 answer:
Csc ( x ) - cot ( x ) = ( 1 / sin ( x) ) - ( cos (x) / sin (x) )
= ( 1 - cos (x) ) / sin (x)
then 1 - cos (x) = 2 sin^2 ( x/2 )
and sin x = 2sin( x/2)cos( x/2)
substitute it
= ( 1 - cos (x) ) / sin (x)
=2 sin^2 ( x/2 ) / 2sin( x/2)cos( x/2)
then simplify
= sin (x/2) / cos (x/2)
since sin/cos = tan
csc ( x ) - cot ( x ) = tan ( x/2)
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