If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1,` then `(gof)(x)` is ____________

The period of the function f(x)=c^(sin^2x+(sin(x+pi/3))^2+cosxcos(x+pi/3)) is (where c is constant) 1 (b) pi/2 (c) pi (d) cannot be determined

Let f(x)=sin[pi/6sin(pi/2sinx)] for all x in RR

If 2 sin^(2)(x-(pi)/(3))-5sin(x-(pi)/(3))+2lt0 , then belongs tp

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=

If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)(x), then the reciprocal of g^(prime)((-7)/6) is_________

If sin^(-1)x+sin^(-1)y=(2pi)/(3)",then"cos^(-1)x+cos^(-1)y is equal to

If 2 sin^(2) ((pi//2) cos^(2) x)=1-cos (pi sin 2x), x ne (2n + 1) pi//2, n in I , then cos 2x is equal to

Let f(x)=sin^(23)x-cos^(22)xa n dg(x)=1+1/2tan^(-1)|x| . Then the number of values of x in the interval [-10pi,8pi] satisfying the equation f(x)=sgn(g(x)) is __________

Let f(x)=sin^(23)x-cos^(22)xa n dg(x)=1+1/2tan^(-1)|x| . Then the number of values of x in the interval [-10pi,8pi] satisfying the equation f(x)=sgn(g(x)) is __________