Pré-Vestibular ⇒ (PUC) Trigonometria: Expressão Trigonométrica

[Doug]

O valor de [tex3]\frac{1}{1+\text{sen}^2 x}+\frac{1}{1+\cos^2 x}+\frac{1}{1+\sec^2 x}+\frac{1}{1+\text{cossec}^2x}[/tex3] é:

a) [tex3]0[/tex3]
b) [tex3]1[/tex3]
c) [tex3]3[/tex3]
d) [tex3]4[/tex3]
e) [tex3]2[/tex3]

[Thales Gheós]

• [tex3]\frac{1}{1+s^2}+\frac{1}{1+c^2}+\frac{1}{1+\frac{1}{c^2}}+\frac{1}{1+\frac{1}{s^2}}[/tex3]
  
  [tex3]\frac{1}{1+s^2}+\frac{1}{1+c^2}+\frac{c^2}{1+c^2}+\frac{s^2}{1+s^2}[/tex3]
  
  [tex3]\frac{1+s^2}{1+s^2}+\frac{1+c^2}{1+c^2}=2[/tex3]