1.

If `theta=pi/(4n)` then the value of `tanthetatan(2theta)tan(3theta)....tan((2n-1)theta)` is

Answer» Correct Answer - 1
`2n theta=pi//2`
`:. theta,(2n-1)theta=(pi//2)-theta`
`or 2theta,(2n-2)theta=(pi//2)-2theta,...`
They form complementary angles A and B so that `tanA tanB=tanAcotA=1` for each pair.
Also, `tanntheta=tan. Pi/4=1`
Hence, the value of product is 1


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