Question

solve this question plz

Answer 1

Given x sin theta = y cos theta ------------------------ (1)

Given xsin^3 theta + ycos^3 theta = sintheta cos theta can be written as

x sin theta * sin^2 theta + y costheta * cos^2 theta = sin theta * cos theta  ------ (2)

Substitute (1) in (2), we get

y cos theta * sin^2 theta + y cos theta * cos^2 theta = sin theta * cos theta

y cos theta(sin^2 theta + cos^2 theta) = sin theta * cos theta

y cos theta(1) = sin theta * cos theta

y = sin theta  ------------------- (3)


Substitute (3) in (1), we get

x sin theta = y cos theta

x sin theta = sin theta * cos theta

x = cos theta   ------------------- (4).


Now,

x^2 + y^2 = sin^2 theta  + cos^2 theta

                 = 1.


LHS = RHS


Hope this helps!

Answer 2

HELLO DEAR,




x sin³A+ y cos³A = sinA.cosA

=> (x sin A). sin²A+ (y cos A). cos²A = sinA.cosA

=> (x sin A). sin²A+ (x sin A). cos²A = sinA.cosA

 [Using x sin A - y cos A = 0 = x sin A = y cos A ]

=> (x sin A)(sin²A+ cos²A) = sinA.cosA  

=> (x sin A)(1) = sinA.cosA

=> x  = cosA



 (x sin A = y cos A )

= >cos A. sin A = y cos A

[using the above result] 

=> y = sin A 


x² + y² = (cos A)² + (sin A)² = cos² A + sin² A = 1

I HOPE ITS HELP YOU DEAR,
THANKS