Evaluate `cosAcosB-sinAsinB`

If tanA=(1)/(sqrt(3))andtanB=sqrt(3) ,then find the value of cosAcosB-sinAsinB

If in triangle A B ,cosAcosB+sinAsinBsinC=1. Show that a : b : c=1:1:sqrt(2)

If A=60^(@) and B=30^(@) , verify that : (i)sin(A+B)=sinAcosB+cosAsinB (ii) cos(A+B)=cosAcosB-sinAsinB

Using vector method prove that cos(A-B)=cosAcosB+sinAsinB

In a triangle ABC if cos A cosB+sinAsinB sinC=1 show that the sides are in the proportion 1:1:sqrt(2)

If sin(A+B)=sinAcosB+cosAsinB and cos(A-B)=cosAcosB+sinAsinB , find the values of (i) sin75^(@) and (ii) cos15^(@) .

If A=60^(@) and B=30^(@) , verify that : (i)sin(A-B)=sinAcosB-cosAsinB (ii) cos(A-B)=cosAcosB+sinAsinB (iii) tan(A-B)=(tanA-tanB)/(1+tanAtanB)

If in a /_\ ABC, cosA.cosB+sinA.sinB.sinC =1,then (A) A=B (B) C=pi/2 (C) AC=BC (D) AB=sqrt(2) AC