`sinx/(sin2xsin3x)+sinx/(sin3xsin4x)+sinx/(sin4xsin5x)+....n` terms is equal to

sin(5x)/sinx

sinx+sin3x+sin5x=0

sinx+sin3x+sin5x=0

int2sin3xsin6xdx=

" int sinx sin 2x (sin3x)dx

int sin xsin3xdx=

If |(sinx,sin2x,sin3x),(sin2x,sin3x,sinx),(sin3x,sinx,sin2x)|=0 then the number of values of x in interval [0,2pi] is

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

(sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

sin2x+2sin4x+sin6x= 4cos^(2)xsin4x