If `(cos^2x+1/(cos^2x))` `(1+tan^2 2y)(3+sin3z)=4,` then `x` is an integral multiple of `pi` `x` cannot be an even multiple of `pi` `z` is an integral multiple of `pi` `y` is an integral multiple of `pi/2`

If (cos^2 x + 1/(cos^2 x)) (1 + tan^2 2y)(3 + sin 3z) = 4 ,then

f(x)=(cosx)/([(2x)/pi]+1/2), where x is not an integral multiple of pi and [dot] denotes the greatest integer function, is an odd function an even function neither odd nor even none of these

If x-y =(4n +1) (pi)/(4) (where n is an integer) and (x+y) is not an odd multiple of pi/2, then the value of (sin 2x -sin 2y)/(cos 2x+ cos 2y) is -

If dy/dx+3/cos^2xy=1/cos^2x,x in((-pi)/3,pi/3)and y(pi/4)=4/3," then "y(-pi/4) equals

f(x)= cosx/([2x/pi]+1/2) where x is not an integral multiple of pi and [ . ] denotes the greatest integer function, is (a)an odd function (b)an even function (c)neither odd nor even (d)none of these

2 sin^2(pi/2 cos^2 x) = 1 - cos(pi sin 2x) . if

f(x)=cos^2x+cos^2(pi/3 +x)-cosxcos(pi/3 +x) is

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi and x+y+z=(3)/(2) , then show that, x=y=z.

If cos(x+pi/3)+cos x=a has real solutions, then (a) number of integral values of a are 3 (b) sum of number of integral values of a is 0 (c) when a=1 , number of solutions for x in [0,2pi] are 3 (d) when a=1, number of solutions for x in [0,2pi] are 2

The value of the integral sqrt2 int_0^pi sqrt(1-cos2x) dx is ?