Question

if tan theta=2xy/x^2-y^2,prove that sin theta=2xy/x^2+y^2​

Answer 1

ǫᴜᴇsᴛɪᴏɴ :-

$if \: tanθ = \frac{2xy}{x {}^{2} - y {}^{2} } \: \: prove \: that \: sinθ = \frac{2xy}{x {}^{2} + y {}^{2} }$

ᴀɴsᴡᴇʀ :-

$tanθ = \frac{p}{b} = \frac{2xy}{x {}^{2} - y {}^{2} }$

p = 2xy

b = x² - y²

h = ?

by using Pythagoras theorem :

h² = b² + p²

h² = (x² - y²)² + (2xy)²

h² = (x²)² + (y²)² - 2x²y² + 4x²y²

h² = (x²)² + (y²)² + 2x²y²

h² = (x² + y²)²

h = √(x² + y²)²

h = x² + y²

$sin \: θ = \frac{p}{h} = \frac{2xy}{x {}^{2} + y {}^{2} }$

Hᴇɴᴄᴇ Pʀᴏᴠᴇᴅ !