Question

9th one pls.ans it.I will be happy

Answer 1

hey mate here is your answer

Answer 2

My HTM doesn't have theta so if in

HTM I took Alfa instead of theta it would be

$\tan( \alpha ) + \sin( \alpha ) = m \\ \\ \tan( \alpha ) - \sin( \alpha ) = n \: \\ \\ m \times n = { \tan}^{2} \alpha - { \sin}^{2} \alpha \\ \\ mn = \frac{ { \sin }^{2} \alpha }{ { \cos }^{2} \alpha } - { \sin}^{2} \alpha \\ \\ mn = { \tan}^{2} \alpha \times { \sin }^{2} \alpha \\ \\ \sqrt{mn} = \tan( \alpha ) \sin( \alpha ) \\ \\ \\ m + n = 2 \tan( \alpha ) \\ \\ m - n = 2 \sin( \alpha ) \\ \\ lhs \\ {m}^{2} - {n}^{2} \\ \\ =( m + n)(m - n) \\ \\ = 2tan \alpha \times 2 \sin \alpha \\ \\ = 4 \tan( \alpha ) \sin( \alpha ) \\ \\ = 4 \sqrt{mn} \\ \\ = rhs$

HOPE WOULD HELP