Question

if tan a + sin a= m and tan a - sin a =n show that m square - n square = 4√ mn

Answer 1

putting value of m &n in equation,
(tanA+sina)2-(tana-sina)2
tan2a+sin2a+2tanasina-tan2a-sin2a+2tanasina
=4tanasina=LHS
now putting value of m&n in 2nd equation,
4√(tana-sina)(tana+ sina)
on solving,
=4tanasina=RHS
do both sides are equal.
Hence proved
Hope it will help you