Question

If xsin3theta+ycos3theta=sintheta cos theta and xsintheta = ycos theta, prove that x2 +y2 =1

Answer 1

$here \: is \: your \: answer \: mate$

$given \: x. \sin(a) = y \cos(a) ...........1$

$let \: x {sin}^{2}(a) \: + y \cos(a) \times {cos}^{2}a \: = \sin(a) \times \cos(a) \\ x {sin}^{3} + xsin \: a \: \times {cos}^{2} a = \sin(a) \times \cos(a) .......from(1)$

$x {sin}^{3} a + xsin \: a(1 - {sin}^{2} a) = \sin(a) \times \cos(a)$

$x {sin}^{3} a \: + xsin \: a \: - x {sin}^{3} = \sin(a) \times \cos(a)$

$xsin \: a \: = \sin(a) \times \cos(a) \\ x = cos \: a \: .........(2)$

$by \: subsituting \: this \: value \: in \: (1) \\ we \: get \: y = sin \: a$

$so \: \: {x}^{2} + {y}^{2} = {sin}^{2} a \: + {cos}^{2} a \: = 1$

$please \: mark \: as \: brainlist$