Let a-cos-isin- then prove that an-1an-2cos n- for n being natural number-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration by Substitution

Let a=cosα+...

Question

Let $a = cos α + i sin α$ then prove that $a^{n} + \frac{1}{a^{n}} = 2 cos n α$ for $n$ being natural number.

Open in App

Solution

Suggest Corrections

Similar questions

1 + 2 + 3 + . . . . . + n = \frac{n (n + 1)}{2}

n

(a_{n}) n \geq 1

a_{2 n} = a_{n} + n

n \geq 1

a_{n}

a_{n} = n,

n \geq 1.

Prove that $c o s α + c o s (α + β) + c o s (α + 2 β) + . . . . . + c o s (α + (n - 1) β)$

$= \frac{c o s {α + \frac{n - 1}{2} β} s i n (\frac{n β}{2})}{s i n \frac{β}{2}}$ for all n $ϵ$ N.

n

1, 2, 3, 4, \dots, n

14.

n

{⟨ a_{n} ⟩}_{n \geq 0}

a_{0} = 0, a_{1} = 1

a_{n} = 2 a_{n - 1} + a_{n - 2}

n \geq 2

m > 0

0 \leq j \leq m

2 a_{m}

a_{m + j} + (- 1)^{j} a_{m - j}

2^{k}

n

n

k

2^{k}

a_{n}

Join BYJU'S Learning Program