Prove that the length of perpendiculars from points 'P(m^2,2m) Q (mn ,m+n) and R(n^2,2n)' to the line `x cos^2theta+ysinthetacostheta+sin^2theta=0` are in G.P.

The lengths of the perpendiculars from the points (m^(2), 2m), (mn, m+n) and (n^(2), 2n) to the line x+sqrt3y+3=0 are in

Prove that the lengths of the perpendiculars from the points (m^2,2m),(m m^(prime),m+m^(prime)), and (m^(prime2),2m^(prime)) to the line x+y+1=0 are in GP.

Prove that the lengths of the perpendiculars from the points (m^2,2m),(m m^(prime),m+m^(prime)), and (m^('2),2m^(prime)) to the line x+y+1=0 are in GP.

If p_(1),p_(2),p_(3) be the length of perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^('2),2m') respectively on the line xcosalpha+ysinalpha+(sin^(2)alpha)/(cosalpha)=0 then p_(1),p_(2),p_(3) are in:

If p and q are the lengths of perpendicular from the origin to the line xcos(theta)-ysin(theta)=kcos(2theta) and xsec(theta)+ycosec(theta)=k respectively , then prove that p^2+4q^2=k^2

If p and q are the lengths of perpendiculars from the origin to the lines xcostheta-ysintheta=kcos2theta and xsec""theta+y" cosec"""theta=""k , respectively, prove that p^2+4q^2=k^2 .

If (2^n+1)theta=pi then 2^n costheta cos2theta cos2^2 theta .......cos 2^(n-1) theta=

If p and q are respectively the perpendiculars from the origin upon the striaght lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = a cos 2 theta , then 4p^(2) + q^(2) is equal to

If p and q are respectively the perpendiculars from the origin upon the striaght lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = acos 2 theta , then 4p^(2) + q^(2) is equal to

If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.