Question

tan thita +sin thita =m and tan thita -sin thita=n find m square -n square

Answer 1

Given

$\tan \theta +\sin \theta =m\\ \tan \theta -\sin \theta =n$

Now,

$m^2-n^2=(\tan \theta +\sin \theta)^2 -(\tan \theta -\sin \theta)^2\\ m^2-n^2=(\tan^2 \theta +\sin^2 \theta+2\tan \theta\sin \theta) -(\tan^2 \theta +\sin^2 \theta-2\tan \theta\sin \theta)\\ m^2-n^2=4\tan \theta\sin \theta$