Question

Prove that tan(A+B)*tan(A-B)=cos²B-cos²A/cos²B-sin²A?

Answer 1

Please refer to a Proof in the Explanation.

Explanation:

Recall that,

`(1) : sin(x+y)sin(x-y)=sin^2x-sin^2y=cos^2y-cos^2x.`

`(2) : cos(x+y)cos(x-y)=cos^2x-sin^2y=cos^2y-sin^2x.`

We will use the latter parts of the above Identities.

`:. tan(A+B)tan(A-B)={sin(A+B)/cos(A+B)}{sin(A-B)/cos(A-B)},`

`=(cos^2B-cos^2A)/(cos^2B-sin^2A).`