Answer :
First, we expand the equation:
[tex] cos^{2}A+2cosAcosB+ cos^{2}B+sin^{2}A+2sinAsinB+sin^{2}B[/tex]
Then, we combine certain terms in order to simplify them using trigonometry identities.
[tex]cos^{2}A+sin^{2}A+cos^{2}B+sin^{2}B+2cosAcosB+2sinAsinB[/tex]
Note these identities:
Pythagoran relation: [tex]cos^{2}A+sin^{2}A = cos^{2}B+sin^{2}B=1[/tex]
Sum and Difference Formula/Identities: [tex]cos(A-B) = cosAcosB+sinAsinB[/tex]
Thus, if we apply these identities, the simplified equation would be:
[tex]2(cos(A-B))+2[/tex]
Simplying further, the answer would be
[tex]2[cos(A-B)+1][/tex]
[tex] cos^{2}A+2cosAcosB+ cos^{2}B+sin^{2}A+2sinAsinB+sin^{2}B[/tex]
Then, we combine certain terms in order to simplify them using trigonometry identities.
[tex]cos^{2}A+sin^{2}A+cos^{2}B+sin^{2}B+2cosAcosB+2sinAsinB[/tex]
Note these identities:
Pythagoran relation: [tex]cos^{2}A+sin^{2}A = cos^{2}B+sin^{2}B=1[/tex]
Sum and Difference Formula/Identities: [tex]cos(A-B) = cosAcosB+sinAsinB[/tex]
Thus, if we apply these identities, the simplified equation would be:
[tex]2(cos(A-B))+2[/tex]
Simplying further, the answer would be
[tex]2[cos(A-B)+1][/tex]