If ABC are angles of a triangle such that x = cis A, y = cis B, z = cis C, then find value of xyz

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Solution

Given:-
$x = c i s A$
$y = c i s B$
$z = c i s C$
To find:- $x y z = ?$
Solution:-
Since $A, B$ and $C$ are angles of a triangle.
Therefore,
$A + B + C = 180 °$
$x y z$
$= c i s A \cdot c i s B \cdot c i s C$
$= c i s (A + B + C)$
$= c i s 180 °$
$= cos 180 ° + i sin 180 °$
$= - 1 + i (0) = - 1$
Hence the value of $x y z$ is $- 1$ .

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