VANIANTATUNT ) Also took tan "I t tant 2

The function f (t) = tan t -t :

If x= a(cos t + tsin t), y= a(sin t- t cos t) , then dy/dx .............. A) cot t B) -tan t C) sqrt (tan t) D) tan t

Q.34 Q.34 Show that the roots r,s and t of the cubic Show that the roots r,s and t of the cubic x(x-2) (3x-7) 2, are real and positive. Also compute the value of tan-(r) + tan-(s) + tan (t) the value oftan ()+ tan(s)+ tan(0)

If (tan(I n6)dottan(I n2)dot"tan"(I n3))/(tan(I n6)-tan(I n2)-"tan"(I n3))=k , then the value of k is________

In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (i) The total number of students.

Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx)i se q u a lto (tant)/(2t) (b) (tant)/(t^2) (c) tan t/(2t^2) (d) (t a tt^2)/(2t^2)

Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx)i se q u a lto (tant)/(2t) (b) (tant)/(t^2) (c) tan t/(2t^2) (d) (t a tt^2)/(2t^2)

If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^2) and (d^2y)/(dx^2)  at t =pi/4.