Answer :

We know that the maximum value of Acosα + Bsinα + c is


c + √(A2 +B2)


And the minimum value is c - √(a2 +B2).


(i) Given f(x) = 12 sin x – 5 cos x


Here A = -5,B = 12 and c = 0





-13 12 sin x - 5 cos x ≤ 13


Hence, the maximum and minimum values of f(x) are 13 and -13 respectively.


(ii) Given f(x) = 12 cos x + 5 sin x + 4


Here A = 12,B = 5 and c = 4





-9 ≤ 12 cos x + 5 sin x + 4 ≤ 17


Hence, the maximum And minimum values of f(x) are 17 And -9 respectively.


(iii) Given


We know that sin(A -B) = sinA cosB - cosA sinB





Here





-3 ≤ 11


Hence, the maximum And minimum values of f(x) are 11 And -3 respectively.


(iv) Given f(x) = sin x – cos x + 1


Here A = -1,B = 1 And c = 1





Hence, the maximum And minimum values of f(x) are And respectively.


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