exo7 3908

Soient \(\alpha,\beta,\gamma \in \R\) tels que \(\alpha+\beta+\gamma = \pi\).

1

Démontrer que : \(1 - \cos\alpha + \cos\beta + \cos\gamma = 4\sin\frac\alpha2 \cos\frac\beta2 \cos\frac\gamma2\).

2

Simplifier \(\tan\frac\alpha2 \tan\frac\beta2 + \tan\frac\beta2 \tan\frac\gamma2 + \tan\frac\gamma2 \tan\frac\alpha2\).