Prove that the function: `f(x)=cos^2x+cos^2(pi/3+x)-cosx*cos(pi/3+x)` is constant function. Find the value of that constant

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

The value of cos^(2)x + cos^(2) (pi/3 + x) - cos x *cos(pi/3+ x) is

Prove that the function f(x)=cos x is strictly decreasing in (0,pi)

Prove that the function f(x)=cos x is strictly increasing in (pi,2 pi)

Period of the function f(x) = sin((pi x)/(2)) cos((pi x)/(2)) is

Write the range of the function f(x)=cos[x] where -(pi)/(2)

If x in (0,pi//2) , then the function f(x)= x sin x +cosx +cos^(2)x is

Find the value of x for which the function f(x)=1+2sin x+3cos^(2)x(0<=x<=(2 pi)/(3)) ) is maximum.Also find these values of the function.