Home
Class 12
MATHS
Find the maximum value of 4sin^2x+3cos^2...

Find the maximum value of `4sin^2x+3cos^2+sinx/2+cosx/2dot`

Text Solution

Verified by Experts

We have
`S=4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2)`
`=3+sin^(2)x+sin""(x)/(2)+cos""(x)/(2)`
`=3+sin^(2)x+sqrt(2)sin((pi)/(4)+(x)/(2))`
Clearly, maximum value of S occurs when `x=(pi)/(2)`.
So, `S_("max")=3+1+sqrt(2)=4+sqrt(2)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.1|11 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.2|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the maximum value of 4sin^(2)x+3cos^(2)x+sin((x)/(2))+cos((x)/(2))

Find the minimum and maximum values of sin2x-cos2x

Find the minimum and maximum values of 3cos x+4sin x

Find the maximum and minimum value of 3 sin 2x+4 cos 2x+3 .

Find maximum and minimum values of 9cos^(2)x + 48 sinx cosx - 5 sin^(2)x - 2 .

find least value of 2^sinx +2^cosx

Maximum value of cosx (sinx +cos x) is equal to :

The maximum value of (3cosx+4sinx) (3sinx-4cosx) for every x in R is

Find the value of int_0^(pi/2)(sinx.cosx)/((a^2cos^2x+b^2sin^2x)^2)dx

If 0ltxlt(pi)/(2) then the minimum value of (cos^(3)x)/(sinx)+(sin^(3))/(cosx)(x)/(x) , is