Question

If x sin^3 theta+y cos^3 theta=Sin theta x cos theta and x sin theta =y cos theta,then show that x^2+y^2=1

Answer 1

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

Answer 2

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

Step-by-step explanation:

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