Write the principal value of `t a n^(-1)[t a n(3pi)/4]dot`

For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi The principal value of cos^(-1) (cos 5t^(2)) is

If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a n A t a n B t a n Cdot

If x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t), find the values of (dy)/(dx) at t=(pi)/(4) and t=(pi)/(3)

If f(n)=int_(0)^(x)[cos t]dt, where x in(2n pi,2n pi+(pi)/(2));n in N and [*] denotes the greatest integer function.Then, the value of f((1)/(pi))| is ...

The value of lim_(n rarr oo)(1)/(n^(2)){(sin^(3)pi)/(4n)+2(sin^(3)(2 pi))/(4n)+...+n(sin^(3)(n pi))/(4n)} is equal to

The instantaneous velocity of a particle moving in a straight line is given as a function of time by: v=v_0 (1-((t)/(t_0))^(n)) where t_0 is a constant and n is a positive integer . The average velocity of the particle between t=0 and t=t_0 is (3v_0)/(4 ) .Then , the value of n is

Write the second term of the sequence t_(n) = 2n + 1 .

The Fibonacci sequence is defence by t_(1)=t_(2)=1,t_(n)=t_(n-1)+t_(n-2)(n>2). If t_(n+1)=kt_(n) then find the values of k for n=1,2,3 and 4.