Home
Class 12
MATHS
If a in (0,1)a n df(a)=(a^2-a+1)+(8sin^2...

If `a in (0,1)a n df(a)=(a^2-a+1)+(8sin^2a)/(sqrt(a^2-a+1))+(27 cos e c^2a)/(sqrt(a^2-a+1))` , then the least value of `(f(a))/2` is_______

Text Solution

Verified by Experts

The correct Answer is:
18
Using `A.M.ge G.M.` (forpositive numbers)
`(s^2-a+1)+(8sin^2a)/sqrt(a^2-a+1)+(27cosec^2a)/sqrt(a^2-a+1)`
`ge 3((a^2-a+1)(8sin^2a)/(sqrt((a^2a+1)))(27cosec^2a)/sqrt((a^2-a+1)))^(1/3)`
`=3(2^3 3^3 )^(1/3)=3(6)=18`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives JEE Main|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives JEE Advanced single correct answer type|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|3 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If cos 2theta=(sqrt(2)+1)(cos theta-(1)/(sqrt(2))) , then the general value of theta(n in Z)

1. sin^(-1)((1)/(sqrt(2))) 2. cos^(-1)((sqrt(3))/(2))

cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

If the value of the definite integral int_0^1(sin^(-1)sqrt(x))/(x^2-x+1)dx is (pi^2)/(sqrt(n)) (where n in N), then the value of n/(27) is

If 0ltAltBltpi, sin A-sinB=(1)/(sqrt2) and cos A-cos B=sqrt((3)/(2)) , then the value of A+B is equal to

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value of f(1) will be

find the value of sin^(-1)(-sqrt3/2)+cos^(-1)(sqrt3/2)

The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)} is

The minimum value of the function f(x)=(sinx)/(sqrt(1-cos^2x))+(cosx)/(sqrt(1-sin^2x))+(tanx)/(sqrt(sec^2x-1))+(cotx)/(sqrt(c o s e c^2x-1)) whenever it is defined is