Find the value of - 2 -1 6 - - 2 -1 6-

Using binomial expansion ( √( 2 ) +1 ) #160; ^ 6 =^ 6 C _ 0 2 ^ 3 +^ 6 C _ 1 ( √( 2 ) #160; ) #160; ^ 5 +^ 6 C _ 2 ( √( 2 ) #160; ) #160; ^ 4 ...

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Binomial Expression

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Question

Find the value of ${(\sqrt{2} + 1)}^{6} - {(\sqrt{2} - 1)}^{6}$ .

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Solution

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(\sqrt{2} + 1)^{6} + (\sqrt{2} - 1)^{6}

Find the value of $s i n^{2} \frac{π}{16}$ + $s i n^{2} \frac{2 π}{16}$ + $s i n^{2} \frac{3 π}{16}$ +..... $s i n^{2} \frac{16 π}{16}$

\frac{16 \times 2^{n + 1} - 4 \times 2^{n}}{16 \times 2^{n + 2} - 2 \times 2^{n + 2}} .

{cos}^{2} \frac{π}{16} + {cos}^{2} \frac{3 π}{16} + {cos}^{2} \frac{5 π}{16} + {cos}^{2} \frac{7 π}{16}

t a n^{2} \frac{π}{16} + t a n^{2} \frac{2 π}{16} + t a n^{2} \frac{3 π}{16} + . . . . . . + t a n^{2} \frac{7 π}{16}

{(\frac{2 + s e c 20^{o}}{c o s e c 20^{o}})}^{2}

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