Question

If 4x=cosecA and 4/x=cotA . Find the value of 4[x² - 1/x²]

Answer 1

Step-by-step explanation:

$Given: \\4x=cosec \: A \implies \: x = \frac{cosec \: A}{4} \\ and \\ \frac{4}{x} =cot \: A \implies \: \frac{1}{x} = \frac{cot \: A}{4} \\ \therefore \: 4\{ {x}^{2} - \frac{1}{ {x}^{2} } \} = 4\{(\frac{cosec \: A}{4})^{2} - (\frac{cot \: A}{4})^{2} \} \\ = 4\{\frac{cosec^{2} \: A}{16} - \frac{cot^{2} \: A}{16}) \} \\ = \frac{4}{16} \{cosec^{2} \: A -cot^{2} \: A \} \\ = \frac{1}{4} \times 1 \\ = \frac{1}{4} \\ Thus, \\ 4\{ {x}^{2} - \frac{1}{ {x}^{2} } \} =\frac{1}{4}$