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

1 Answer
Nov 16, 2016

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