If `p\ and\ q` be the perpendicular form the origin upon the straight lines `x s e ctheta+ycosectheta=a\ and\ xcostheta-y sintheta=acos2theta` Prove that : `4p^2+q^2=a^2\ dot`

If p_1a n d\ p_2 are the lengths of te perpendiculars from the origin upon the lines x\ s e ctheta+h y cos e ctheta=a\ a n d\ xcostheta-ysintheta=acos2theta respectively, then a.4p1 2+p2 2=a^2 b. p1 2-4p2 2=a^2 c. p1 2+p2 2=a^2 d. none of these

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 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 the lengths of perpendiculars from the origin to the lines xcostheta-ysintheta=kcos2theta and xsectheta+yc o s e ctheta=k , respectively, 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 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

The equation of the straight line passing through the point (acos^3theta,asin^3theta) and perpendicular to the line xsectheta+ycos e ctheta=a is (A) xcostheta-ysintheta=acos2theta (B) xcostheta+ysintheta=acos2theta (C) xsintheta+ycostheta=acos2theta (D) none of these

Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+sectheta)^2=7+tan^2theta+cot^2theta

Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+sectheta)^2=7+tan^2theta+cot^2theta

If x=cos e ctheta-sintheta and y=cosec^ntheta-sin^ntheta, then show that (x^2+4)((dy)/(dx))^2=n^2(y^2+4)dot