Prove by vector method that `cos(A+B)cos AcosB-sinAsinBdot`

Prove by vector methods. cos(A- B) = cos A cos B + sin A sin B.

Prove by vector method that the diagonals of a rhombus bisect each other at right angles.

Prove that cos2A=cos^2 A -sin^2 A

Prove that cos3A=4cos^3 A-3cosA

Prove by vector method that median to the base of an isoscels triangle is perpendicular to the base.

Prove by vector method that sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta.

Prove by vector method that an angle in a semi-circle is a right angle.

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

By vector method, prove that cos (alpha+Beta) = cosalphacosBeta-sinalphasinBeta .

Prove by vector method that the perpendiculars (altitudes) from the vertices to the sides of a triangle are concurrent.