Question

calculando-se a expressão 1/sen(105graus)-cos (75graus) obtem-se

Answer 1

sen 105° = sen (60° + 45°) =
sen 60°.cos 45° + sen 45°.cos 60° =
1/2.√2/2 + √2/2.√3/2 =
√2/4 + √6/4

cos 75° = cos (45° + 30°) =
cos 45°.cos 30° - sen 45°.sen 30° =
√2/2.√3/2 - √2/2.1/2 =
√6/4 - √2/4

sen 105° - cos 105° =
√2/4 + √6/4 - [√6/4 - √2/4] =
√2/4 + √6/4 - √6/4 + √2/4 =
√2/2

1/(sen 105° - cos 75°) =
1/(√2/2) =
2/√2 =
2/√2 . √2/√2 =
2√2/2 =
√2.