Prove that the point `{(a)/(2)(t+(1)/(t)), (b)/(2)(t-(1)/(t))}` lies on the hyperbola for all values of `t(tne0)`.

Show that the point : x=(2rt)/(1+t^2), y=(r(1-t^2))/(1+t^2) (r constant) lies on a circle for all values of t such that -1 le t le 1 .

Show that the points (at_(1)^(2),2at_(1)) , (at_(2)^(2),2at_(2)) and (a,0) are collinear if t_1t_2 =-1 .

If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)) , where t is the variable quantity, then the locus of P is

lim_(t to0)(1-(1+t)^(t))/(In (1+t)-t) is equal to

Prove that: t a n 70^0=t a n 20^0+2t a n 50^0dot

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

Find whether the points (-a,-b),[-(s+1)a,-(s+1)b] and [ (t-1)a,(t-1)b] are collinear?

Prove that t_(75) = 2 t_(50) for 1^(st) order reaction.

If sinx = (2t)/(1+t^2), tan y = (2t)/(1-t^2) , find dy/dx

The interval in which f(x)=int_(0)^(x){(t+1)(e^(t)-1)(t-2)(t+4)} dt increases and decreases