Question

If cos(A+B)=cos A cos B-sin A sin B, what is the value of cos 120°?​

Answer 1

Answer:Solution

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We can prove this by using euler’s identity : e  

ix

=cosx+i sinx

therefore we have e  

iA

=cosA+i sinA,

and e  

iB

=cosB+isinB

now

e  

iA

∗e  

iB

=e  

i(A+B)

 

⇒(cosA+i sinA)(cosB+i sinB)=(cos(A+B)+i sin(A+B))

⇒(cosA∗cosB−sinA∗sinB)+i(sinA∗cosB+cosA∗sinB)=(cos(A+B)+i sin(A+B))

On equating the imaginary parts on both sides of the equation we get the required result

i.e.sin(A+B)=sinA∗cosB+cosA∗sinB

Step-by-step explanation: