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`        If p , p’ are the lengths of the perpendiculars from the origin from the straight line, whose equations are xsecR+ycosecR=a amd xosR-ysinR=acos2R, then show that 4p2 + 4p’2=a2 .`
3 years ago

Arun Kumar
IIT Delhi
256 Points
```										Hello Student$\\p'= { acos^2R \over \sqrt{sin^2R+cos^2R}}=|acos^2R| \\p=|{ a \over \sqrt{sec^2R+cosec^2R} }|=|{ asinRcosR }|=|{asin2R \over 2}| \\=>4p^2 + 4p'^2 \\=>4(a^2cos^4R+{a^2sin^22R \over 4}) \\=>cos^2R={1 +cos2R \over 2} \\=>4a^2( { 1/4+1/4+cos2R/2})=4a^2(1+cos2R)/2= \\=>4a^2cos^2R$Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty
```
3 years ago
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