Let `f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)/(sqrt(4+sqrt(2x-1))-2)` .Determine the value of p, if possible, so that the function is continuous at `x = 1/2`.

Find the period of f(x)=sin((pix)/(n !))-cos((pix)/((n+1)!))

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is

If f(x) = (1 - cos x)/(1+ cos x) " then " f (pi/2) = ............ .

If f(x) = (1 - cos x)/(1+ cos x) " then " f (pi/2) = ............ .

Fnind the domain of f(x) =(1)/(1-2 cos x) .

Let f(x)=(2cosx-1)(2cos2x-1)(2cos2^2x-1).... (2cos2^(n-1) x-1), (where ngeq1)dot Then prove that f((2pik)/(2^n+-1))=1AAk in Idot

Let f(x)=log(2x-x^2)+sin(pix)/2dot Then which of the following is/are true? Graph of f is symmetrical about the line x=1 Maximum value of f is1. Absolute minimum value of f does not exist. none of these

Let f(x)=sin^(-1)((2x)/(1+x^(2))) and g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1)) . Then tha value of f(10)-g(100) is equal to

Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer function. Then the range of f(x) is

Let f(x)=cos(a_1+x)+1/2cos(a_2+x)+1/(2^2)cos(a_1+x)++1/(2^(n-1))cos(a_n+x) where a)1,a_2 a_n in Rdot If f(x_1)=f(x_2)=0,t h e n|x_2-x_1| may be equal to pi (b) 2pi (c) 3pi (d) pi/2