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The maximum value of 5 cosx + 3cos(x + 60) + 3 is a) 5 b) 11 c) 10 d) -1


The maximum value of 5 cosx + 3cos(x + 60) + 3 is


a)      5


b)      11


c)      10


d)      -1


Grade:

2 Answers

vikas askiitian expert
509 Points
10 years ago

5cosx + 3cosx+60 + 3

5cosx + 3[cosxcos60 - sinxsin60] + 3

5cosx + 3[cosx/2 - (root3/2)sinx] + 3

(13/2)cosx - (3root3/2)sinx + 3

 

let 13/2 = a & 3root3/2 = b then

expression becomes

acosx - bsinx + 3

maximum value of this type of expression is equal to

[a2+b2]1/2+3 = maximum value

 

after plugging values of a,b we get

491/2+3 = max value

 10 = max value

 -4 = minimum value

 

option c) is correct

ankit singh
askIITians Faculty 614 Points
one year ago

Explanation:

5cosα+3cos(α+π3)+3

=5cosα+3(cosαcos(π3)sinαsin(π3))+3

=132cosα323sinα+3

#= sqrt( (13/2)^2+ (3/2sqrt3)^2) (cos alpha cos beta - sin alpha

sin beta ) + 3#

=7cos(α+β)+3,β=arccos(1314)

As cosine value [1,1], the maximum of the given function

=max7[1,1]+3=7+3=10

graph{(5 cos x + 3 cos ( x + pi/3 ) +3 - y )(y-10+0x)= 0[-10 10

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