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|Exercise JEE Main Previous Year|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • TRIGONOMETRIC EQUATIONS

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

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|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)

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

If x=sin^(-1)(a^6+1)+cos^(-1)(a^4+1)-tan^(-1)(a^2+1),a in R , then the value of sec^2x is_______

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

Find the value of cot^(-1)(1)+sin^(-1)((-sqrt(3))/(2))-sec^(-1)(-sqrt(2))

(8)/(sqrt(1 - (4 x)^(2))) + (27)/(sqrt(1 - 9 x^(2))) - (15)/(1+ 25 x^(2))

Prove that (tan^(-1)1/e)^2+(2e)/((e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^2+1))

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x