Question

Prove that: 2 sin 2 A + sin 4 A / 2 sin 2 A - sin 4 A = cot square A Guys ! Plz help me with this question

Answer 1

✪ᴀɴsᴡᴇʀ✪

$L. H. S.$

$=\frac{2sin(2A) + sin(4A)} {2sin(2A) - sin(4A)}$

$=\frac{2sin(2A) + 2sin(2A)cos(2A)} {2sin(2A) - 2sin(2A)cos(2A)}$

$=\frac{2sin(2A)[1 + cos(2A)]} {2sin(2A)[1 - cos(2A)]}$

$=\frac{[1 + cos(2A)]} {[1 - cos(2A)]}$

$=\frac{2cos^2(A)} {2sin^2(A)}$

$=\frac{cos^2(A)} {sin^2(A)}$

$=cot^2(A)$

$= R. H. S.$

Hence Proved