Question

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

Answer 1

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

Ans: -1

Explanation:

`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`