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Question Number 193385 by AnshKumar last updated on 12/Jun/23

	Answered by som(math1967) last updated on 12/Jun/23

	$L . H . S$ $= \frac{s e c 8 A - 1}{s e c 4 A - 1}$ $= \frac{\frac{1}{c o s 8 A} - 1}{\frac{1}{c o s 4 A} - 1}$ $= \frac{c o s 4 A (1 - c o s 8 A)}{c o s 8 A (1 - c o s 4 A)}$ $= \frac{c o s 4 A \times 2 {s i n}^{2} 4 A}{c o s 8 A \times 2 {s i n}^{2} 2 A}$ $= \frac{2 s i n 4 A c o s 4 A s i n 4 A}{2 {s i n}^{2} 2 A c o s 8 A}$ $= \frac{2 s i n 2 A c o s 2 A \times s i n 8 A}{2 {s i n}^{2} 2 A \times c o s 8 A}$ $= c o t 2 A \times t a n 8 A$ $= \frac{t a n 8 A}{t a n 2 A} = R . H . S$
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