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

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

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