Prove by vector methods that `sin(alpha+beta)=sin alphacos beta+cos alphasin beta`

Prove by vector methods that sin(alpha+beta)=sin alpha cos beta+cos alpha sin beta

What is sin (alpha+beta) - 2 sin alpha cos beta + sin(alpha- beta) =

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=

Prove that cos(alpha-beta)/(cos alpha sin beta)=tan alpha+cot beta

Prove,by induction,that sin alpha+cos(alpha+beta)-sin(alpha+2 beta)-cos(alpha+3 beta)+sin(alpha+4 beta)+... to n terms

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=

If alpha,beta are complementary angles and sin alpha=(3)/(5), then sin alpha cos beta-cos alpha sin beta=

(cos alpha + cos beta)/( sin alpha - sin beta) + (sin alpha + sin beta)/( cos alpha - cos beta ) =

Evaluate: quad =|cos alpha cos beta cos alpha sin beta-sin alpha-sin beta cos beta0sin alpha cos beta sin alpha sin beta cos alpha|

If alpha,beta are complementary angles, sin alpha=(4)/(5), then sin alpha cos beta+cos alpha sin beta=