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The maximum value of 5 cosx + 3cos(x + 60) + 3 is
a) 5
b) 11
c) 10
d) -1
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
5cosα+3cos(α+π3)+3
=5cosα+3(cosαcos(π3)−sinαsin(π3))+3
=132cosα−32√3sinα+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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