Home
Class 12
MATHS
The minimum value of sqrt((3s in x-4cosx...

The minimum value of `sqrt((3s in x-4cosx-10(3sinx+4cosx-1))` is ________

Text Solution

Verified by Experts

The correct Answer is:
7
`f(x) =9sin^2x-16cos^2x-10(3sinx-4cosx)-10(3sinx+4cosx)+100`
`25 sin^2x-16cos^2x+84`
`=(5sinx-6)^2+48`
The minimum value of f(x) occurs when sin x = 1
Therefore , the minimum value of `sqrt(f(x)) is 7`.
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

The minimum value of sqrt((3sin x-4cosx-10)(3sinx+4cosx-10)) is ________

Evaluate: int1/(sqrt(3)sinx+cosx)dx

Evaluate int(3sinx+2cosx)/(3cosx+2sinx)dx.

Evaluate int(sqrt(tanx))/(sinx cosx)dx

Evaluate: int((3sinx-2)cosx)/(5-cos^2x-4sinx)\ dx

Find the minimum value of the function f(x)=(1+sinx)(1+cosx),AAx inR .

Evaluate: int(x-sinx)/(1-cosx)dx

Solve sinx +cosx =1

Find the maximum value of sqrt(3)sinx+cosx and x for which a maximum value occurs.

Solve 8sinx=(sqrt(3))/(cosx)+1/(sinx)