Question

who will answer this question ur answer will be termed as brain list

Answer 1

x*sin³ (A) + y*cos³ (A) = sin (A) * cos (A) and x sin (A) = y cos (A) 
=> x*sin (A) * sin² (A) + y*cos (A) * cos² (A) = sin (A) * cos (A)
=> x*sin (A) * sin² (A) + x sin (A) * cos² (A) = sin (A) * cos (A) ; as y cos (A) =x sin (A) 
=> x*sin (A) [sin² (A) + cos² (A) ] = sin (A) * cos (A)
=> x *sin (A) * [1] = sin (A) * cos (A) ; sin (A) gets cancelled as sin (A) is not = 0
=> x = cos (A)

Also we have ; x sin (A) = y cos (A) ; or
=> cos (A) * sin (A) = y cos (A) 
=> y = sin (A) 

Therefore x² + y² = cos² (A) + sin² (A) = 1
=> x² + y² = 1.