Number of roots of the equation 3-cos x2- 4-2sin 8x-x- -0-5- -are

(3+cos x ) ^ 2 =4 2sin ^ 8 x where x ∈ [0,5π ] (3+cos x ) ^ 2 ∈ [4,16] as 1≤ sin x ≤ 1 , 1≤ cos x ≤ 1 4 2sin ^ 8 x ...

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

Byju's Answer

Standard XII

Mathematics

Derivative of Standard Functions

Number of roo...

Question

Number of roots of the equation $(3 + cos x)^{2} = 4 - 2 {sin}^{8} x, x ϵ [0, 5 π]$ are

Open in App

Solution

${(3 + cos x)}^{2} = 4 - 2 {sin}^{8} x w h e r e x \in [0, 5 π]$

${(3 + cos x)}^{2} \in [4, 16] a s - 1 \leq sin x \leq 1, - 1 \leq cos x \leq 1$

$4 - 2 {sin}^{8} x \in [2, 4]$

$S o b o t h c a n b e e q u a l o n l y w h e n b o t h a r e e q u a l t o 4$

$T h e n sin x = 0 a n d cos x = 1 a t t h e s a m e t i m e .$

$x = (0, 2 π, 4 π}$

$W e h a v e t h r e e s o l u t i o n s$

Suggest Corrections

Similar questions

Q. The equation

(3 + cos x)^{2} = 4 - 2 {sin}^{8} x

has

Q. Number of roots of the equation

| sin x cos x | + \sqrt{2 + {tan}^{2} x + {cot}^{2} x} = \sqrt{3}, x ϵ [0, 4 π]

are,

Q. The number of solution of the equation

sin 2 x - 2 cos x - 4

in the interval

[0, 5 π]

Q. The number of real roots of the equation

e^{sin x} - e^{- sin x} - 4 = 0

are?

Find the number of positive real roots for equation 3 $x^{5}$ - 4 $x^{4}$ - 42 $x^{3}$ + 56 $x^{2}$ + 27x - 36 = 0. If all the roots of above given equation are real.

Join BYJU'S Learning Program

Number of roots of the equation (3+cosx)2=4−2sin8x,xϵ[0,5π]are

(3+cosx)2=4−2sin8xwherex∈[0,5π](3+cosx)2∈[4,16]as−1≤sinx≤1,−1≤cosx≤14−2sin8x∈[2,4]Sobothcanbeequalonlywhenbothareequalto4Thensinx=0andcosx=1atthesametime.x=(0,2π,4π}Wehavethreesolutions

Number of roots of the equation $(3 + cos x)^{2} = 4 - 2 {sin}^{8} x, x ϵ [0, 5 π]$ are