The coordinate axes are rotated about the origin (0,0) in counter clockwise direction through an angle of 600. lf p and q are intercepts made on new axes by a straight line whose equation referred to the original axes is x+y=1, then 1p2+1q2=
When axes are rotated through 600, co-ordinates are
x=xcosθ−ysinθ=x2−y√32
y=xsinθ−ycosθ=x√32−y2
∴x+y=1⇒x2−y√32+x√32+y2=1
x(1+√3)2+y(1−√3)2=1
p=21+√3;q=21−√3
1p2=1+3+2√34;1q2=1+3−2√34
∴1p2+1q2=4+44=2