Prove that `(sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0`

Prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0

Prove that, sin51^(@)+cos81^(@)=cos21^(@)

Prove that, (cos7A+cos5A)/(sin7A-sin5A)=cotA

Prove that, sin^(2)A+sin^(2)B+cos^(2)(A+B)+2sinAsinBcos(A+B)=1

Prove that, sinA+sin2A+sin4A+sin5A= 4cos((A)/(2))cos((3A)/(2))sin3A .

Prove that (cos(9x)-cos(5x))/(sin(17x)-sin(3x))=-(sin(2x))/(cos(10x))

sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x)) = _______

Prove that : (cos80^(@))/(sin10^(@))+cos59^(@)cosec31^(@)=2

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C