Prove that cos(A-B) = cos A CosB + Sin A sin B

1.	Prove that cos(A-B) = cos A CosB + Sin A sin B
Answer» To prove: COS(A-B)= cosA.cosb+sinA.sinB LHS: Cos(A-B) =SIN(90-(A-B)) =sin(90-A+b) =sin((90-A)+B) ; [sin(a+b)=sina.cosb+cosa.sinb] =sin(90-A).cosB+sinB.cos(90-A) ; [sin(90-A)=cosA ; cos(90-A)=sinA] =cosA.cosB+sinA.sinB =RHS ∴LHS=RHS, hence proved.

Answer»

To prove:

COS(A-B)= cosA.cosb+sinA.sinB

LHS: Cos(A-B)

=SIN(90-(A-B))

=sin(90-A+b)

=sin((90-A)+B) ; [sin(a+b)=sina.cosb+cosa.sinb]

=sin(90-A).cosB+sinB.cos(90-A) ; [sin(90-A)=cosA ; cos(90-A)=sinA]

=cosA.cosB+sinA.sinB

=RHS

∴LHS=RHS, hence proved.

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Prove that cos(A-B) = cos A CosB + Sin A sin B​

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Prove that cos(A-B) = cos A CosB + Sin A sin B