Skills JEE - Trigonometria

por Alberto Nascente Sáb 19 Nov 2022, 09:48

Se

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, então calcule

S/ gabarito.

Penso que talvez uma soma telescópica deva resolver, porém, não enxergo nenhuma possível fatoração...
Além de que ele não me diz nada sobre os ângulos

Obrigado! Very Happy

por **tales amaral** Sáb 19 Nov 2022, 11:07

[latex]\forall i ( -1 \leq \cos \theta_i \leq 1)[/latex]
O valor máximo de [latex]\sum_{i = 1} ^n \cos\theta_i[/latex] é n (todos iguais a 1), portanto [latex]\forall i ( \cos \theta_i = 1) \implies \forall i (\sin\theta_i = 0 )[/latex].

A soma do seno é zero.

por Alberto Nascente Sáb 19 Nov 2022, 11:33

Mas Tales, pq disso?

Pensei que, pra provar isso, deveria ter que provar por indução ou algo assim...
Pensei que eu ñ pudesse considerar os ângulos como sendo sempre máximos

por **tales amaral** Seg 21 Nov 2022, 15:57

Alberto Nascente escreveu:Mas Tales, pq disso?

Pensei que, pra provar isso, deveria ter que provar por indução ou algo assim...
Pensei que eu ñ pudesse considerar os ângulos como sendo sempre máximos

Verdade. O problema é que eu não sei qual princípio me permite afirmar isso Neutral

. Vou deixar essa para os universitários!