sin(A-B)=sin A cos B-cos A sin B

Ifsin(A-B)= sin A cosB-cos A sin B and cos(A-B) = cosA cosB + sin A sin B. Find the values of sin 15^@ and cos 15^@ .

Using the fact that sin(A+B)=sin A,A,cos B+cos A sin B and the differentiation,obtain the sum formula for cosines.

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

For all values of angle A and B(i)cos(A-B)=cos A cos B+sin A sin B(ii)cos(A+B)=cos A cos B-sin A sin B

Prove that sin(A+B+C)=sin A cos B cos C+cos A sin B cos C+cos A cos B sin C-sin A sin B sin Ccos(A+B+C)=cos A cos B cos C-cos A sin B sin C-sin A cos B sin C-sin A sin B cos C

If det [[cos (A + B), - sin (A + B), cos2Bsin A, cos A, sin B-cos A, sin A, cos B]] = 0

If det [[cos (A + B), - sin (A + B), cos2Bsin A, cos A, sin B-cos A, sin A, cos B]] = 0

If A = 60 ^(@) and B = 30 ^(@) , find the value of (sin A cos B+ cos A sin B)^(2) + (cos A cos B - sin A sin B )^(2)

Prove that : cos (A + B) = cos A cos B - sin A sin B .

Prove that : cos (A - B) = cos A cos B + sin A sin B .