Question

If xsin³¢ + ycos³¢ = sin¢cos¢ and xsin¢ = ycos¢ , prove that x²+y²= 1.

Answer 1

Here It Is...
genius

Answer 2

Heya !!!


X Sin³ theta + Y Cos³ theta = Sin theta × Cos theta


=> (X Sin theta) Sin²theta + (Y cos theta) Cos²theta = Sin theta × Cos theta

=> (X sin theta) Sin²theta + (X sin theta) Cos²theta = Sin theta × Cos theta [ Y cos theta = X sin theta ]


=> (X Sin theta) (Sin²theta + Cos²theta) = Sin theta× Cos theta


=> X sin theta × 1 = Sin theta × Cos theta

=> X sin theta = Sin theta × Cos theta


=> X = Sin theta × Cos theta/Sin theta


=> X = Cos theta--------(1)


Now,

X sin theta = Y cos theta


=> Cos theta × Sin theta = Y cos theta [ X = Cos theta]

=> Y = Cos theta × Sin theta/Cos theta

=> Y = Sin theta -----------(2)


To prove :- X² + Y² = 1


LHS = X² + Y²



(Cos)² + (Sin)²


=> 1

Hence,

LHS = RHS = 1...... PROVED....



HOPE IT WILL HELP YOU....... :-)