Advertisements
Advertisements
Question
The minimum value of 3cosx + 4sinx + 8 is ______.
Options
5
9
7
3
Advertisements
Solution
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
RELATED QUESTIONS
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
In a ∆ABC, prove that:
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
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:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
`cosec x = 1 + cot x`
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
The smallest positive angle which satisfies the equation
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
