" (v) "int_(0)^((pi)/(2))(2log sin x-log sin2x)dx=-(pi)/(2)log2

int_(0)^((pi)/(2))(2log cos x-log sin2x)dx

int_(0)^((pi)/(2))log(sin x)dx

int_(0)^(pi//2) (2logsin x - log sin 2x) dx=

int_(0)^((pi)/(2))log(sin2x)dx

int_(0)^((pi)/(2))cos2x log sin xdx

Show that int_(0)^((pi)/(2))log(sin2x)dx=-(pi)/(2)(log2)

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(2log sin x-log sin2x)dx

int_(0)^(pi//2) log sin x dx =

int_(0)^((pi)/(2))(sin8x log(cot x))/(cos2x)dx