Home
Class 12
MATHS
Let f(x)=2cos e c2x+secx+cos e cxdot The...

Let `f(x)=2cos e c2x+secx+cos e cxdot` Then find the minimum value of `f(x)forx in (0,pi/2)dot`

Text Solution

Verified by Experts

`f(x)=2co sec 2 x +sec x +co secx`
`=2 co sec 2x+(sqrt(secx)-sqrt(co sec x))^(2)+(2sqrt(2))/(sqrt(2cos x.sinx))`
`therefore =2 co sec 2x+(sqrt(secx)-sqrt(co sec x))^(2)+2sqrt(2)sqrt(co sec 2x)`
Clearly, minimum value occurs for `x=(pi)/(4)`, as for this value of x,
`sqrt(sec x)=sqrt(co secx)=0` and `co sec 2x=1`.
So, `f_("min"(x=(pi)/(4))=2(sqrt(2)+1)`
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

Let f(x)=2cos ec2x+sec x+cos ecx, then the minimum value of f(x) for x in(0,(pi)/(2)) is

Find the maximum and minimum value of f(x)=sin x+(1)/(2)cos2x in [0,(pi)/(2)]

Find the maximum and minimum values of f(x)=sin x+(1)/(2)cos2x in [0,pi/2]

If f(x)=3+cos^-1(cos(pi/2+x)cos(pi/2-x)+sin(pi/2+x)sin(pi/2-x)) , x in [0,pi] then find the minimum value of f(x) is

"Let f(x) "=|{:(cos x" " sin x" " cos x),(cos 2x" "sin 2x" "2cos 2x),(cos 3x" "sin 3x" "3cos 3x):}|" Then find the vlue of "f'(0) and f'(pi//2).

"Let f(x) "=|{:(cos x" " sin x" " cos x),(cos 2x" "sin 2x" "2cos 2x),(cos 3x" "sin 3x" "3cos 3x):}|" Then find the vlue of "f'(0) and f'(pi//2).

" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f(0) and f' (pi//2) .

Let f(x)=sin x+2cos^(2)x,x in[(pi)/(6),(2 pi)/(3)] then maximum value of f(x) is

The minimum value of f(x)-sin^(4)x+cos^(4)x,0lexle(pi)/(2) is

Let 0