Question

If x sin ³ ∅ + y cos³ ∅ = sin∅cos∅ and x * sin∅ = y * cos∅ then prove that x² + y² = 1

Answer 1

Answer:

given that x sin = y cos.

=> x = y × cos/sin = y cot.

and y = x × sin/cos = x tan.

we have to prove that x²+ y²= 1

Step-by-step explanation:

x = ycot, and y = xtan.

Taking L.H.S

x² + y² = (ycot)² + (xtan)²

= y²×cot² + x²×tan²

=> y²cot² + x² × 1÷cot²

=> y²cot² + x² = cot²

=> y²cot² = cot² - x²

=> y² + x² = cot²/cot²

:- x² + y² = 1

HENCE, PROVEN.