Question

if x sin cube theta + Y cos cube theta is sin theta cos theta and x sin theta is Y cos theta, prove that X square + Y square is 1​

Answer 1

EASY

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