If A B C are the angles of a triangle, and a, b, c are the corresponding sides, then the real part of $ (acosB+bcosA + i(asinB-bsinA))^n $is?
My book says that the real part of this is $(acosB+bcosA) ^ n = c^n$
But if you expand this expression using the binomial theorem , won't there be more terms not containing 'i'?
Please explain.
Hint: Using sine Law of triangle, $a\cos B+b\cos A =2R\sin(A+B)=c$
and $a\sin B=b\sin A$