Home
Class 12
MATHS
find the range of function f(x)=sin(x+(p...

find the range of function `f(x)=sin(x+(pi)/(6))+cos(x-(pi)/(6))`

Text Solution

Verified by Experts

`f(x)=sin(x+(pi)/(6))+cos(x-(x)/(6))`
`=sin x cos(pi)/(6)+cos x sin(pi)/(6)+cos x cos (pi)/(6)+sin x sin(pi)/(6)`
`=(sqrt(3)+1)/(2) (sin x+cos x)`
Now, `sin x+cos x in [-sqrt(2),sqrt(2)]`
`therefore f(x)=(sqrt(3)+1)/(2)(sin x+cos x)in[-sqrt(2)xx(sqrt(3)+1)/(2),sqrt(2)xx(sqrt(3)+1)/(2)]`
or `f(x)in[-(sqrt(3)+1)/(sqrt(2)),(sqrt(3)+1)/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 range of the function f(x)=(1)/(1-3 cos x)

Find the range of the function f(x)=(1)/(2+sin3x) .

Find the range fo the function f(x)=(x^(2)-x-6)/(x-3)

Find the range of the function f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).

Find the range of the function f(x) =x Sin x-(1)/(2) sin^(2) x for x in (0,(pi)/(2))

The fundamental period of the function f(x)=4cos^4((x-pi)/(4pi^2))-2cos((x-pi)/(2pi^2)) is equal to :

Find the range of the function f(x)=4cos^(3)x-8cos^(2)x+1 .

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

The number of integral values in the range of the function f(x)=sin^(-1)x-cot^(-1)x+x^(2)+2x +6 is

Find the range of the function f(x)=6^x+3^x+6^(-x)+3^(-x)+2.