Question

if 4x =sec theta and 4/x=tan theta then find the value of 16(x²-1÷x²)​

Answer 1

Explanation:

$4x = \sec( \alpha ) \\ \\ = > (4x) {}^{2} = \sec {}^{2} ( \alpha ) \\ \\ = > 16x {}^{2} = \sec {}^{2} ( \alpha ) \\ \\ \frac{4}{x} = \tan( \alpha ) \\ \\ = > ( \frac{4}{x} ) {}^{2} = \tan {}^{2} ( \alpha ) \\ \\ = > \frac{16}{x {}^{2} } = \tan {}^{2} ( \alpha ) \\ \\ 16(x {}^{2} - \frac{1}{x {}^{2} } ) \\ \\ = 16x {}^{2} - \frac{16}{x {}^{2} } \\ \\ = \sec {}^{2} ( \alpha ) - \tan {}^{2} ( \alpha ) \\ \\ = 1 \\ \\ \\ formula \: \: - \: \: (\sec {}^{2} ( \alpha ) - \tan {}^{2} ( \alpha ) ) = 1$