itestepsfEbnsuutiolndisu27. If x si n° + y cos' θ = sin θ cos θ an

1.	itestepsfEbnsuutiolndisu27. If x si n° + y cos' θ = sin θ cos θ and x sin θ = y cos θ then prove thatx' + y-1.28 ell sl 1
Answer» xsin³∅ + ycos³∅ = sin∅. cos∅x.sin³∅ + cos²∅.(ycos∅) = sin∅.cos∅use xsin∅= ycos∅ in above xsin³∅ + cos²∅.xsin∅ = sin∅.cos∅ xsin∅( sin²∅ + cos²∅) = sin∅.cos∅ xsin∅ = sin∅.cos∅ x = cos∅ so, y = sin∅ now we know, sin²∅ + cos²∅ = 1 put sin∅ = y cos∅ = x hence, x² + y² = 1

itestepsfEbnsuutiolndisu27. If x si n° + y cos' θ = sin θ cos θ and x sin θ = y cos θ then prove thatx' + y-1.28 ell sl 1

Answer»

xsin³∅ + ycos³∅ = sin∅. cos∅x.sin³∅ + cos²∅.(ycos∅) = sin∅.cos∅use xsin∅= ycos∅ in above

xsin³∅ + cos²∅.xsin∅ = sin∅.cos∅ xsin∅( sin²∅ + cos²∅) = sin∅.cos∅ xsin∅ = sin∅.cos∅ x = cos∅ so, y = sin∅

now we know, sin²∅ + cos²∅ = 1 put sin∅ = y cos∅ = x

hence, x² + y² = 1