Question

prove it (tan+cot)^2-(tan-cot)^2 =4

Answer 1

$( \tan \alpha + \cot \alpha ) {}^{2} - ( \tan \alpha - \cot \alpha) {}^{2} \\ = (\tan {}^{2} \alpha + 2 \tan \alpha \cot \alpha + \cot {}^{2} \alpha) - ( \tan \alpha {}^{2} - 2 \tan \alpha \cot \alpha + \ \cot {}^{2} \alpha ) \\ = \tan {}^{2} \alpha + 2 \tan\alpha \cot \alpha + \cot {}^{2} \alpha - \tan {}^{2} \alpha + 2 \tan \alpha \cot \alpha - \cot {}^{2} \alpha \\ = 4 \tan \alpha \cot \alpha \\ = 4 \: \: \: \: \: (because. \: \tan \alpha \cot \alpha = 1 ) \\ so.......this \: is \: proven........ \\ hope \: this \: helps........ \\ if \: correct.....mark \: as \: brainlist$

Answer 2

drashti5 gave correct answer