The locus of the point ` ( a cos theta, b sin theta ) ` where ` 0 le theta lt 2 pi ` is

The locus of the point ( a cos ^3 theta, b sin ^ 3 theta ) where 0 le theta lt 2pi is

The locus of the point (cot theta + cos theta, cot theta - cos theta ) where 0 le theta lt 2 pi is

The locus of the point (cosec theta - sin theta, sec theta - cos theta ) where 0 le theta lt 2pi is

The locus of the point (a sec theta, b tan theta ) where 0 le theta lt 2pi is

The locus of the point ( a cos theta + b sin theta, a sin theta - b cos theta ) where 0 le theta lt 2pi is

The locus of the point ( a sec theta + b tan theta , bsec theta +atan theta) where 0 le theta lt 2pi is

If cos theta - sin theta=1/5 , where 0 lt theta lt pi/4 , then:

sin theta -2 = cos2theta when 0 le theta le 2pi

sin theta + sin 5 theta = sin 3theta (0 le theta le 2pi)

If cos theta - sin theta = (1)/(5) , where 0 lt theta lt (pi)/(4) , then