Question #57b0f

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Answer 1 · 2017-02-07T20:48:01

see below

Left Hand Side:

Use the formulas:
$sin x - sin y = 2 cos (1/2 (x+y) )sin (1/2 (x-y))$
$cos x + cos y = = 2 cos ( 1/2 (x+y)) cos (1/2 (x-y))$

$(cosx+cosy)/(sinx-siny)=(2cos(1/2 (x+y))*cos(1/2 (x-y)))/(2cos(1/2 (x+y))*sin(1/2 (x-y)))$

$=(cancel(2cos(1/2 (x+y)))*cos(1/2 (x-y)))/(cancel(2cos(1/2 (x+y)))*sin(1/2 (x-y)))$

$=cos(1/2 (x-y))/(sin(1/2 (x-y))$

$=cot (1/2 (x-y))$

$:.=$ Right Hand Side