Prove that #2cot(x/2) (1-cos^2(x/2))#is identical to #sinx# ?

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Answer 1 · 2018-03-19T14:23:50

See below.

We will use the following identities:

#cotA:=1/tanA=cosA/sinA#

#sin^2A+cos^2A=1#

#sinA=2sin(A/2)cos(A/2)#

Start of proof

#2cot(x/2)(1-cos^2(x/2))#

#=2cos(x"/"2)/sin(x"/"2)sin^2(x/2)#

#=2cos(x/2)sin(x/2)#

#=sinx#, as required.