Question

Verify the identity: Use the fundamental , sum-difference , & double-angle identities in the steps.

tan8k - tan8k tan²4k = 2tan4k

Answer 1

Firstly take out tan8k as common..

Tell me what you are left with??

Answer 2

tan 8k ( 1- tan²4k)

Answer 3

Yes..

Now use this formula for tan8k..

\[\tan2A = \frac{2tanA}{1 - \tan^2A}\]

Answer 4

8k = 2A

So, A = 4k..

Use the above formula where A = 4k..