" 7.Prove the following ":(sin alpha-sin beta)/(cos beta-cos alpha)=cot(alpha+beta)/(2)" ."

Suppose alpha,beta and theta are angles satisfying 0

Suppose alpha,beta a n d theta are angles satisfying 0 < alpha < theta < beta < pi/2 dot Then prove that (sin alpha-sin beta)/(cos beta-cos alpha)=-cot theta

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

Prove that (cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2) ((alpha+beta)/(2))

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|

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

Prove that (cos alpha+cos beta)^(2)+(sin alpha+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

Evaluate ,,,|cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha,cos beta,sin alpha sin beta,cos alpha]|

det[[cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha cos beta,sin alpha sin beta,cos alpha]]

Prove that : (cos alpha+cos beta)^(2)+(sin alpha+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))