How can I verify this identity? Thanks!

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Answer 1 · 2018-04-21T17:55:37

The answer is #"option A"#

#sinx-siny=2sin((x+y)/2)cos((x-y)/2)#

#cosx-cosy=-2sin((x+y)/2)sin((x-y)/2)#

Therefore,

#LHS=(sinx-siny)/(cosx-cosy)#

#=(2sin((x+y)/2)cos((x-y)/2))/(-2sin((x+y)/2)sin((x-y)/2))#

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

#=-cot((x-y)/2)#

The answer is #"option A"#