IF xsin3A + ycos3A = sinA*cosA

& xsinA = ycosA

Prove x2 + y2 = 1

 

If xcosA/a + ysinA/b = 1

& xsinA/a -ycosA/b = 1

Prove x2/a2 + y2/b2 = 2

Asked by Shreyash.98rana | 18th Aug, 2014, 01:26: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n space x sin cubed A plus y cos cubed A equals sin A cross times cos A R e w r i t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma open parentheses x sin A close parentheses sin squared A plus open parentheses y cos A close parentheses cos squared A equals sin A cross times cos A rightwards double arrow open parentheses y cos A close parentheses sin squared A plus open parentheses y cos A close parentheses cos squared A equals sin A cross times cos A space space open square brackets sin c e space x sin A equals y cos A close square brackets rightwards double arrow y cos A open square brackets sin squared A plus cos squared A close square brackets equals sin A cross times cos A rightwards double arrow y cos A equals sin A cross times cos A rightwards double arrow y equals sin A rightwards double arrow x equals cos A space space open square brackets sin c e space x sin A equals y cos A close square brackets rightwards double arrow x squared plus y squared equals 1

Answered by Vimala Ramamurthy | 18th Aug, 2014, 04:46: PM