Advertisements
Advertisements
प्रश्न
The minimum value of 3cosx + 4sinx + 8 is ______.
विकल्प
5
9
7
3
Advertisements
उत्तर
The minimum value of 3cosx + 4sinx + 8 is 3.
Explanation:
The given expression is 3cosx + 4sinx + 8
Let y = 3cosx + 4sinx + 8
⇒ y – 8 = 3cosx + 4sinx
Minimum value of y – 8 = `sqrt((3)^2 + (4)^2`
⇒ y – 8 = `-sqrt(9 + 16)` = – 5
⇒ y = 8 – 5 = 3
So, the minimum value of the given expression is 3.
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\tan x = \frac{a}{b},\] show that
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
In a ∆ABC, prove that:
In a ∆ABC, prove that:
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If sec x + tan x = k, cos x =
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of points of intersection of the curves
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is
General solution of \[\tan 5 x = \cot 2 x\] is
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
