Let Fn - - -k - 0n 1-4Ksin4 2k- then which of the following is true

The correct option is C F_4 ( 3 π/2 ) = 1 F_n (θ) = sin^4 θ + sin^4 2 θ/4 + sin^4 (2^2 θ)/4^2 + sin^4 (2^3 θ)/4^3 ........ F_2 ( π/4 ) = 1/4 + ...

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

Byju's Answer

Standard XII

Mathematics

Definition of Functions

Let Fn θ = ...

Question

Let $F_{n} (θ) = n \sum k = 0 \frac{1}{4^{K}} {sin}^{4} (2^{k} θ)$ , then which of the following is true

F_{2} (\frac{π}{4}) = \frac{1}{\sqrt{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

F_{3} (\frac{π}{8}) = \frac{2 + \sqrt{2}}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

F_{4} (\frac{3 π}{2}) = 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

F_{5} (π) = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $F_{4} (\frac{3 π}{2}) = 1$
$F_{n} (θ) = {sin}^{4} θ + \frac{{sin}^{4} 2 θ}{4} + \frac{{sin}^{4} (2^{2} θ)}{4^{2}} + \frac{{sin}^{4} (2^{3} θ)}{4^{3}} . . . . . . . .$
$F_{2} (\frac{π}{4}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}$
$F_{3} (\frac{π}{8}) = {(\frac{\sqrt{2 - \sqrt{2}}}{2})}^{4} + \frac{1}{16} + \frac{1}{16} = \frac{2 - \sqrt{2}}{4}$
$F_{4} (\frac{3 π}{2}) = 1 + 0 = 1$
$F_{5} (π) = 0$

Suggest Corrections

Similar questions

Q. If

f_{n} (θ) = n \sum r = 0 \frac{1}{4^{r}} {sin}^{4} (2^{r} θ)

, then which of the following alternative(s) is/are correct?

For a positive integer n, let
$f_{n} (θ) = (t a n \frac{θ}{2}) (1 + s e c θ) (1 + s e c 2 θ) (1 + s e c 4 θ) \dots (1 + s e c 2^{n} θ)$ .
Then

For a positive integer n, let $f_{n} (θ) = (t a n \frac{θ}{2}) (1 + s e c θ) (1 + s e c 2 θ) (1 + s e c 4 θ) . . . . . . (1 + s e c 2^{n} θ) . T h e n$

Q. For a positive integer

n,

let

f_{n} (θ) = (tan \frac{θ}{2}) (1 + sec θ) (1 + sec 2 θ) (1 + sec 4 θ) . . . (1 + sec 2^{n} θ) .

Then

Q. If

f_{n} (θ) = \frac{cos \frac{θ}{2} + cos 2 θ + cos \frac{7 θ}{2} + \dots + cos \frac{(3 n - 2) θ}{2}}{sin \frac{θ}{2} + sin 2 θ + sin \frac{7 θ}{2} + \dots + sin \frac{(3 n - 2) θ}{2}},

then which among the following is (are) CORRECT?

Join BYJU'S Learning Program

Let Fn(θ)=n∑k=014Ksin4(2kθ), then which of the following is true

The correct option is C F4(3π2)=1Fn(θ)=sin4θ+sin42θ4+sin4(22θ)42+sin4(23θ)43........F2(π4)=14+14=12F3(π8)=(√2−√22)4+116+116=2−√24F4(3π2)=1+0=1F5(π)=0

Let $F_{n} (θ) = n \sum k = 0 \frac{1}{4^{K}} {sin}^{4} (2^{k} θ)$ , then which of the following is true