Question

How do you verify the identity `cos(A+B)=(1-tanAtanB)/(secAsecB)`?

Answer 1

`cosAcosB-sinAsinB=cosAcosB-sinAsinB`

Explanation:

`cos(A+B)=cosAcosB-sinAsinB`

`(1-tanAtanB)/(secAsecB)=(1/secA)(1/secB)-(tanAtanB)/(secAsecB)`

`(1/secA)(1/secB)=cosAcosB`

`((tanAtanB)/(secAsecB))=((sinA/cosA)(sinB/cosB))/((1/cosA)(1/cosB))=sinAsinB`

`cosAcosB-sinAsinB=cosAcosB-sinAsinB`