`[sin(x-pi)+cos(x-pi//2)]*cos(x-2pi)`=___________.

int_(-pi)^(pi)sin^(2)x.cos^(2)x dx=

sin m((pi)/(2)+x)+cos n((pi)/(2)-x)

The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi/6)dotcospi/6=sin^2pi/6 in interval ((-pi)/2,pi/2) is_________

The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi/6)dotcospi/6=sin^2pi/6 in interval ((-pi)/2,pi/2) is_________

The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

If sin(pi cos x)=cos(pi sin x), then sin2x=

Prove that: (a) (cos(pi+x) cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x (b) cos((3pi)/2 + x)cos(2pi+x){cot ((3pi)/2-x)+cot(2pi+x)}=1