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Sum of N Terms of an AP

The sum of n ...

Question

The sum of n terms $tan y sec 2 y + tan 2 y sec 4 y + tan 4 y sec 8 y + . . . n$ terms

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Solution

$T_{1} = \frac{s i n y}{c o s y c o s 2 y} = \frac{s i n (2 y - y)}{c o s y c o s 2 y} = t a n 2 y - t a n y$
$T_{2} = t a n 4 y - t a n 2 y$
$T_{n} = t a n 2^{n} y - t a n 2^{n - 1} y$
$∴ S_{n} = t a n 2^{n} y - t a n y$

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