`sin(x-pi/6)+cos(x-pi/3)=sqrt3 sinx`

Evaluate of each of the following integrals int_(pi//6)^(pi//3)(sqrt("sin"x))/(sqrt(sinx)+sqrt(cosx))"d"x

Evaluate of each of the following integrals int_(pi//6)^(pi//3)(sqrt("sin"x))/(sqrt(sinx)+sqrt(cosx))"d"x

Prove the following: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

" sin " (x-(pi)/(6)) + " cos " (x-(pi)/(3)) =sqrt(3) " sin " x

Evaluate int_(pi/6)^(pi/3) sqrt(sin x)/(sqrt(sin x)+sqrt(cos x)) d x

Prove that cos((3pi)/4+x)-cos((3pi)/4-x)= -sqrt2 sinx

sin(pi-6x)+sqrt3 sin(pi/2+6x)=sqrt3

sin(pi/3-x)cos(pi/6+x)+cos(pi/3-x)sin(pi/6+x)=1

f (x) = cos ((pi) / (sqrt (3)) sin x + sqrt ((2) / (3)) pi cos x)