Hello, themartinacster!

Welcome aboard!

There are two ways (at least) to prove the identity,

. . neither is pleasant.

Prove: .

[1] Use the Sum-to-Product identities:

. . .

We have: .

The problem becomes: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[2] Use the Compound Angle identities:

. . .

Use them repeatedly to derive these statements:

. .

We have: .

. . .

. . .