Question

Tan theta + sin theta = m and Tan theta - sin theta = n then prove that m square - n square = 4 whole root of mn

Answer 1

Answer:

(Tan A +Sin A)^2 =m^2

(Tan A - Sin A)^2 = n^2

m^2-n^2= tan^2A+sin^2A+2tanAsinA-tan^2A -sin^2A+2tanAsinA

m^2-n^2 = 4tanAsinA or 4sin^2A/cosA................1

TanAsinA = sin^2A/cosA

(Tan A +Sin A)(Tan A - Sin A)= mn

Tan^2A-sin^2A = mn

sin^2A-sin^2Acos^2A/cos^2A = mn

sin^2A(1-cos^2A)/cos^2A = mn

sin^2A/cosA = √mn

put this value of sin^2A/cosA in equation 1

m^2-n^2 = 4√mn

HENCE PROVED