Prove `(i)sin(A+B)+sin(A-B)=2sinAcosB` (ii) `sin(A+B)-sin(A-B)=2cosAsinB`

Prove (i)sin(A+B)+sin(A-B)=2sin A cos B (ii) sin(A+B)-sin(A-B)=2cos A sin B

Prove (i)cos(A+B)+cos(A-B)=2cos A cos B(ii)cos(A-B)-cos(A+B)=2sin A sin B

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

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

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

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

Prove that: sin(A+2B)sinA-sinBsin(2A+B)sinB=sin(A+B)sin(A-B)

Prove that: sin(A+2B)sinA-sinBsin(2A+B)sinB=sin(A+B)sin(A-B)

If A=B=60^@ , verify that (i) cos(A-B)=cosAcosB+sinAsinB (ii) sin(A-B)=sinAcosB-cosAsinB (iii) tan(A-B)=(tanA-tanB)/(1+tanAtanB)

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