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Question

If un=π/201cos2nx1cos2xdx, then find the value of the determinant Δ=∣ ∣u1u2u3u4u5u6u7u8u9∣ ∣

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Solution

un=π201cos2nx1cos2xdxun+un+22un+1=π20(1cos2nx)+(1cos(2n+4)x)2(1cos(2n+2)x)1cos2xdx=π202cos(2n+2)xcos2x+2cos(2n+2)x1cos2xdx=π202cos(2n+2)xdx=2[sin(2n+2)x2n+2]π20=0un+un+22un+1=0Δ=∣ ∣u1u2u3u4u5u6u7u8u9∣ ∣applying C1 C1+C32C2Δ=∣ ∣u1+u32u2u2u3u4+u62u5u5u6u7+u92u8u8u9∣ ∣=∣ ∣0u2u30u5u60u8u9∣ ∣=0

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