If X sin cubed theta + Ycos space cubed theta = sin theta cos theta and X space sin space theta space equals space y space cos space theta, then
(A)X cubed space plus Y cubed equals space 1
(B)X squared minus Y squared equals 1
(C)X squared plus Y squared equals 1
(D)X to the power of 4 plus Y to the power of 4 equals 1

Asked by pkirankumar4321 | 29th Nov, 2015, 01:37: PM

Expert Answer:

begin mathsize 16px style x sin cubed theta plus y cos cubed theta equals sin theta cos theta space space space space space.... left parenthesis 1 right parenthesis S u b s t i t u t i n g space x sin theta equals y cos theta space i n space left parenthesis 1 right parenthesis comma space w e space g e t y cos theta sin squared theta plus y cos cubed theta equals sin theta cos theta rightwards double arrow y cos theta left parenthesis sin squared theta plus cos squared theta right parenthesis equals sin theta cos theta rightwards double arrow y cos theta equals sin theta cos theta rightwards double arrow y equals sin theta space space space space..... left parenthesis 2 right parenthesis S u b s t i t u t i n g space y equals sin theta space i n space e q u a t i o n space x sin theta equals y cos theta comma space w e space g e t x sin theta equals sin theta cos theta rightwards double arrow x equals cos theta space space space space space.... left parenthesis 3 right parenthesis S q u a r r i n g space e q u a t i o n space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space g e t y squared equals sin squared theta space a n d space x squared equals cos squared theta A d d i n g x squared plus y squared equals cos squared theta plus sin squared theta rightwards double arrow x squared plus y squared equals 1 space end style

Answered by Rashmi Khot | 30th Nov, 2015, 10:19: AM