Question

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

Answer 1

For Proof, refer to the Explanation.

Explanation:

`sec(A-B)=1/cos(A-B)=1/(cosAcosB+sinAsinB)`

`=1/{cosAcosB(1+(sinAsinB)/(cosAcosB))},`

`=1/{cosAcosB(1+tanAtanB)},`

`={1/(cosAcosB)}/(1+tanAtanB),`

`rArr sec(A-B)=(secAsecB)(1+tanAtanB).`