How do you simplify $sin( -pi/7 ) * csc ( 15pi / 7 )$ ?

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Answer 1 · 2015-10-28T14:08:53

Simplify $sin (-pi/7).csc ((15pi)/7)$

Ans: -1

$csc ((15pi)/7) = 1/sin ((15pi)/7)$
$sin ((15pi)/7) = sin (pi/7 + (14pi)/7) = sin (pi/7 + 2pi) = sin (pi/7)$
Since sin (-x) = - sin (x), therefor:

$sin (-pi/7).csc ((15pi)/7) = sin (-pi/7)/(sin (pi/7)) = - 1$

How do you simplify sin( -pi/7 ) * csc ( 15pi / 7 )sin( -pi/7 ) * csc ( 15pi / 7 )?