Equation of the line passing through the point `(acos^3theta, a sin^3theta)` and perpendicular to the line `xsectheta + y cosec theta =a` is `xcostheta-ysintheta =acos2theta`.

Answer

False

Explanation

Given points p `(acos^3theta,asin^3theta)` and the line is `xsectheta+ycosectheta= a`
`because` Slope of this line `(-sectheta)/(cosectheta)=tan theta`
and Slope of required line `=(1)/(tantheta)=cottheta`
`therefore `Equation of the required line is
`y-asin^3theta=cottheta (x-acos^3theta)`
`rArrysintheta -asin^4theta =xcostheta-acos^4theta`
`rArrxcostheta-ysintheta=acos^4theta-asin^4theta`
`rArrxcostheta-ysin theta=a[(cos^2theta+sin^2theta)(cos^2theta-sin^2theta)]`
`rArrxcostheta-ysintheta=acos^2theta`
Hence, the given statements is false.