Question

Tantheta +sintheta=m and tantheta-sintheta=n show m square-n square=4√mn

Answer 1

let tantheta = t
& sintheta = s

given,
t + s =m.........(1)
t - s =n...........(2)

squaring equation (1)&(2)

(t+s) square =
m square ......(3)

(t-s) square =
n square ........(4)

now subtracting equation(4)from(3)

(t+s) square - (t-s) square =m square-n square

m square-n square = (t+s) square - (t-s) square

m square-n square=(t^2 +2ts +s^2)-t^2+2ts -s^2

m square-n square=4ts