Verify tan(α+β) = [tan(α)+tan(β)] / [1 + tan(α)tan(β)]
- use the angle sum formula for cosine, the angle sum formula for sine, and the identity tan(x) = sin(x)/cos(x) to verify it.

Proved

Step-by-step explanation:

To Prove:

Proof:

Now:

Therefore:

Applying these angle sum formula

Divide all through by

=sin \alpha cos \beta + cos \alpha sin \beta/cos \alpha cos \beta/cos \alpha cos \beta- sin \alpha sin \beta/cos \alpha cos \beta  

=sin \alpha/cos \alpha + sin \beta/cos \beta/1-tan \alpha tan \beta  

=tan A + tan B/1-tan A tan B

a

step-by-step explanation:

it's