Prove that: `1/(sin(x-a)cos(x-b))=(cot(x-a)+"tan"(x-b))/(cos(a-b))`

Prove that: 1/(sin(x-a)sin(x-b))=(cot(x-a)-"cot"(x-b))/(sin(a-b))

Prove that: 1/(cos(x-a)cos(x-b))=(tan(x-b)-"tan"(x-a))/(sin(a-b))

Prove that: (1)/(sin(x-a)sin(x-b))=(cot(x-a)-cot(x-b))/(sin(a-b))

Prove that: (1)/(cos(x-a)cos(x-b))=(tan(x-b)-tan(x-a))/(sin(a-b))

Prove that : sin cot^(-1) tan cos^(-1) x=x

Prove that : sin cot^(-1) tan cos^(-1) x=x

If int (1)/(sin (x -a ) cos (x -b)) dx = A log | (sin (x -a))/( cos (x -b ))| + B. Then

Prove that: (1+cos4x)/(cot x-tan x)=(1)/(2)sin4x

Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqrt((a-b)/(a+b)) "tan" x/2)

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