MCQ
If $n $ is a positive integer, then ${\left( {\sqrt 3 + 1} \right)^{2n}} - {\left( {\sqrt 3 - 1} \right)^{2n}}$ is
- ✓an irrational number
- Ban odd positive integer
- Can even positive integer
- Da rational number other than positive integers
$1-i=\sqrt{2}\left(\cos \left(-\frac{\pi}{4}\right)+i \sin \left(-\frac{\pi}{4}\right)\right)$
$(1+i)^{n}=(\sqrt{2})^{n}\left(\cos \frac{n \pi}{4}+i \sin \frac{n \pi}{4}\right)$
$(1-i)^{n}=(\sqrt{2})^{n}\left(\cos \left(-\frac{n \pi}{4}\right)+i \sin \left(-\frac{n \pi}{4}\right)\right)$
$(1+i)^{n}+(1-i)^{n}=(\sqrt{2})^{n}\left(2 \cos \frac{n \pi}{4}\right)$
$=2^{\frac{n+2}{2}} \cos \frac{n \pi}{4}$
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Assertion $(A)$ : The circle ${x^2} + {y^2} = 1$ has exactly two tangents parallel to the $x$ - axis
Reason $(R)$ : $\frac{{dy}}{{dx}} = 0$ on the circle exactly at the point $(0, \pm 1)$.
Of these statements