If `(x-a)costheta+ysintheta=(x-a)cosphi+ysinphi=a` and `tan(theta/2)-tan(phi/2)=2b` ,then (a) `y^2=2a x-(1-b^2)x^2` (b)`tan(theta/2)=1/x(y+b x)` (c)`y^2=2b x-(1-a^2)x^2` (d)`tan(phi/2)=1/x(y-b x)`

If (a-b)sin (theta+phi)=(a+b)sin(theta-phi) and a tan. (theta)/(2)-b tan.(phi)/(2)=c , then

If sqrt(1+x^(2))sintheta=x," Prove that "tan^(2)theta+cot^(2)theta=x^(2)+(1)/(x^(2)

If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the focal chord of x^2/a^2-y^2/b^2=1 then prove that tan(x/a)tan(phi/2)=(1-e)/(1+e)

If costheta_1 =2costheta_2, then tan((theta_1-theta_2)/2)tan((theta_1+theta_2)/2) is equal to (a) 1/3 (b) -1/3 (c) 1 (d) -1

If tan theta+sec theta=x" show that 2 tan "theta=x -1/x, 2 sec theta=x+1/x. Hence show that sin theta=(x^(2)-1)/(x^(2)+1)

If x=a sec theta and y=b tan theta then b^(2)x^(2)-a^(2)y^(2) =_____.

if (x)/(2)=(cosA)/(cosB) then prove that (x tan A+y tan B)/(x+y)=tan""(A+B)/(2)

If (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of the ends of a focal chord passing through (ae,0) of x^2/a^2-y^2/b^2=1 then tan(theta/2)tan(phi/2) equals to

(sec2x-tan2x) equals a) tan(x-pi/4) b) tan(pi/4-x) c) cot(x-pi/4) d) tan^2(x+pi/4)

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2