Prove that `(sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(cosAcosB)=0`

Prove that cosAsin(B-C)+cosBsin(C-A)+cosCsin(A-B)=0

Prove that sin(A+B)sin(A-B)=sin^2A-sin^2B

Prove that (sin 3 x+sin x) sin x+(cos 3 x-cos x)cosx=0

For any DeltaABC , prove that (sin(B-C))/(sin(B+C))=(b^2-c^2)/(a^2)

Choose the correct answer from the bracket and fill in the blank sin(B-C)=……………. (sinBcosC+cosBsinC,sinBcosC-cosBsinC , sinBsinC+cosB cosC, sinBsinC-cosBcosC)

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

Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

The value of tan {sin^(-1)(cos(sin^(-1)x))} tan{cos^(-1) (sin(cos^(-1)x))} x in (0,1) a)0 b)1 c)-1 d)None of these

int (dx)/(sin (x-a) sin (x-b)) is :

Prove that sin120^@ cos330^@ +cos240^@ sin330^@=1