Question

If tan +sin = m and tan -sin =n, then prove that m^2-n^2= 4underrootmn​

Answer 1

Step-by-step explanation:

L.H.S: m^2-n^2

(tan +sin)^2-(tan-sin)^2

(tan^2+sin^2+2tan×sin)-(tan^2 +sin^2- 2tan×sin)

4tan×sin

R.H.S : 4 under root mn

4 underrrot (tan +sin) (tan -sin)

4 root tan^2- sin^2

4 root sin^2- sin^2× cos^2 / cos^2

4 root sin^2 ( 1- cos^2)/cos^2

4 root tan^2× sin^2

4 tan×sin

L.H.S = R.H.S

PROVED..