Let f(x)=∣∣∣∣∣ω3ω4ω5sin(m−1)xsinmxsin(m+1)xcos(m−1)xc – InterviewSolution

1.	Let f(x)=∣∣∣∣∣ω3ω4ω5sin(m−1)xsinmxsin(m+1)xcos(m−1)xcosmxcos(m+1)x∣∣∣∣∣,where m∈N and ω is the cube root of unity.If π/2∫0f(x)dx=aω+bω2, then (a,b)=
Answer» Let $f (x) = ∣ ∣∣∣ ∣ \begin{matrix} ω^{3} & ω^{4} & ω^{5} sin (m - 1) x & sin m x & sin (m + 1) x cos (m - 1) x & cos m x & cos (m + 1) x \end{matrix} ∣ ∣∣∣ ∣$ , where $m \in N$ and $ω$ is the cube root of unity. If $π / 2 \int 0 f (x) d x = a ω + b ω^{2},$ then $(a, b) =$

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