Question

If tan a + sin a = m and tan a - sin a = n prove m^2 - n^2 = + or - 4 √mn

Answer 1

Answer:

Step-by-step explanation:

L.H.S= (m^2-n^2)

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

= 4tan sin

R.H.S= 4 root mn

= 4  (tan+sin)(tan-sin) whole in under root

= 4 root (tan^2-sin^2)

= 4 (sin^2/cos^2 -sin^2) whole in under root

= 4 root sin^2-sin^2cos^2/cos ----[cos is not in root it is denominator]

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

= 4 tan (root sin^2)

= 4 tan sin

Therefore, L.H.S = R.H.S