MCQ
If $sin\ x + cos\ x = a$, $a \in \left[ { - \sqrt 2 ,\sqrt 2 } \right] - \left\{ { - 1,1} \right\}$, then
$\sum\limits_{n = 1}^\infty {\left( {{{\sin }^n}\ x + {{\cos }^n}\ x} \right)}$ is equal to -
$\sum\limits_{n = 1}^\infty {\left( {{{\sin }^n}\ x + {{\cos }^n}\ x} \right)}$ is equal to -
- A$\frac{{2(1 + a - {a^2})}}{{{{(a + 1)}^2}}}$
- B$\frac{{2({a^2} - a + 1)}}{{{{(a - 1)}^2}}}$
- C$\frac{{2({a^2} - a + 1)}}{{{{(a + 1)}^2}}}$
- ✓$\frac{{2(1 + a - {a^2})}}{{{{(a - 1)}^2}}}$