If x+iy=(3)/(2+cos theta + sin theta),"p...

If `x+iy=(3)/(2+cos theta + sin theta),"prove that" , x^(2)+y^(2)=4x-3.`

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If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-1.

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If x = sin theta + cos theta sin 2 theta " and " y = cos theta + sin theta sin 2 theta,"prove that " (x+y)^(2//3) + (x-y)^(2//3) = 2

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If x+a= a(2 cos theta-cos 2 theta) and y= a(2 sin theta- sin 2 theta) ,show that (x^(2)+y^(2)+2ax)^(2)=4a^(2)(x^(2)+y^(2)) .

If x=a sin theta and y=b tan theta , then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1 .

If a cos^3theta +3a cos theta sin^2theta =x and asin^3theta+3a cos^2theta sin theta=y prove that (x+y)^(2/3)+(x-y)^(2/3)=2a^(2/3)

If x=cosec theta-sin theta and y=cosec^(n)theta-sin^(n) theta , prove that, (x^(2)+4)((dy)/(dx))^(2)=n^(2)(y^(2)+4) .