Question

1. Prove that
tan 40° + 2 tan 10° = tan 50°​

Answer 1

Step-by-step explanation:

When you're proving an identity you can't treat it like an equation where you can "move" things to the other side. You start with one side and work with it until you've gotten the other side. So, a basic identity is

tan 50 = tan (10 + 40)

= ( tan 10 + tan 40) / ( 1 - tan 10 tan 40)

and another is tan 40 tan 50 = tan 40 cot 40 = 1.

So tan 40 + 2 tan 10 =

tan 40 + tan 10 + tan 10 =

tan 50(1 - tan 40 tan 10) + tan 10 =

tan 50 - tan 50 tan 40 tan 10 + tan 10 =

tan 50 - 1 • tan 10 + tan 10 =

tan 50

HOPE ITS HELPFUL