Question

If xsin³∅ + y cos³ ∅ = sin∅ . Cos∅ and xsin∅ = ycos∅, prove that x² + y² = 1

Answer 1

hope this answer will help you.

Answer 2

Solution

→ x sin∅ = y cos∅ [Given]

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→ x sin³∅ + y cos³∅ = sin∅ cos∅

→ x sin∅(sin²∅) + y cos∅(cos²∅) = sin∅ cos∅

→ x sin∅(sin²∅) + x sin∅(cos²∅) = sin∅ cos∅

→ x sin∅(sin²∅ + cos²∅) = sin∅ cos∅

→ x = cos∅

Now, x sin∅ = y cos∅

→ y = sin∅

→ cos²∅ + sin²∅ = 1 [Identity]

→ x² + y² = 1

Q.E.D