Question

prove: √ sec²O + cosec²O = tanO + cotO​

Answer 1

Answer:

$\sqrt{ \sec {}^{2} (x) + \csc {}^{2} (x) } \\ \\ use \: \:bas ic \: \: identities \: \\ = \sqrt{1 + \cot {}^{2} (x) + 1 + \tan {}^{2} (x) } \\ \\ = \sqrt{ \cot {}^{2} (x) + \tan {}^{2} (x) + 2 } \\ \\ since \: \tan(x) \cot(x) = 1 \\ \\ = \sqrt{ \cot {}^{2} (x) + \tan {}^{2} (x) + 2 \tan(x) \cot(x) } \\ \\ = \sqrt{( \tan(x) + \cot(x)) {}^{2} } \\ \\ = \tan(x) + \cot(x)$