1.

Cos(A-B) =cosA cosB +sinA sinB​

Answer»

Step-by-step explanation:

We WANT to prove that COS(A−B)=cosAcosB+sinAsinB using VECTORS.

Consider vectors OP→ and OQ→ on the unit circle having angles A and B respectively with the positive X axis.

⇒|OP→|=1 and |OQ→|=1, and ALSO,

the angle between OP→ and OQ→ is A−B.

OP→=cosAi^+sinAj^ and OQ→=cosBi^+sinBj^.

OP→⋅OQ→=|OP→||OQ→|cos(A−B)=cos(A−B).

Also, OP→⋅OQ→=(cosAi^+sinAj^)⋅(cosBi^+sinBj^)

=cosAcosB+sinAsinB.

⇒cos(A−B)=cosAcosB+sinAsinB.


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